GCSE Exams Preparation



Volume (H) - QuestionsQ1.?Sanders has a water tank for storing rainwater.The tank is in the shape of a cylinder. The radius of the cylinder is 31 cm. The height of the cylinder is 97.5 cm.The tank is full of water.Work out an estimate for the volume of water in the tank. Give your answer in litres. You must show your working.Use 1000 cm3 = 1 litre. ........................................................... litres?(Total for question = 3 marks)?Q2.Diagram NOT accurately drawnThe diagram shows a prism.All measurements are in cm.All corners are right angles.The volume of the prism is V cm3.Find a formula for V.?????????V = . . . . . . . . . . . . . . . . . . . . . . (Total for Question is 4 marks)Q3.?A can of soup is a cylinder with diameter 7 cm. The can is 10 cm high. The can is full of soup.The soup is poured into a saucepan. The saucepan is a cylinder with diameter 12 cm.Work out the depth of the soup in the saucepan. Give your answer correct to 1 decimal place............................................................ cm? (Total for question = 3 marks)Q4.?* The diagram shows a box for winter grit. The box is in the shape of a cuboid. The box is empty.?Jon wants to fill the box with grit. A bag of grit costs ?2.50 There are 8000 cm3 of grit in a bag.Jon has ?70 to spend on the grit.Does Jon have enough money to buy all the grit he needs to fill the box completely?? (Total for question = 5 marks)Q5.?Jan has some metal that she is going to make into solid metal spheres.Each sphere will have a radius of 2.15 cm.Jan has 1490 cm3 of metal.(a)??Work out an estimate for the number of spheres that Jan can make. ........................................................... (3)(b)??If you calculate the number of spheres accurately, how do you think your answer to part (a) will change?Give a reason for your answer. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. (1)?(Total for question = 4 marks)?Q6.The diagram shows a solid metal cylinder.? Diagram NOT accurately drawnThe cylinder has base radius 2x and height 9x.The cylinder is melted down and made into a sphere of radius r.Find an expression for r in terms of x.????????????????..............................................................................................................................................(Total for Question is 3 marks)Q7.?Jane makes cheese.The cheese is in the shape of a cuboid.Jane is going to make a new cheese.The new cheese will also be in the shape of a cuboid. The cross section of the cuboid will be a 5cm by 5cm square.Jane wants the new cuboid to have the same volume as the 2cm by 10cm by 15cm cuboid.Work out the value of x............................................................? (Total for question = 3 marks)Q8.?Here are two solid spheres, A and B.Sphere A is made of gold. Sphere B is made of silver.Sphere A has radius 2 cm. Sphere B has radius 3 cm.Gold has a density of 19 000 kg/m3Silver has a density of 10 000 kg/m3Which sphere has the greater mass? You must show how you get your answer.?(Total for question = 4 marks)?Q9.?The diagram shows a fish tank in the shape of a cuboid.The dimensions of the tank are 50 cm by 32 cm by 20 cm.The tank is full of water and sand.The ratio of the volume of water to the volume of sand is 5 : 1Work out the number of litres of water in the tank. You must show all your working. ........................................................... litres?(Total for question = 5 marks)?Q10.?The diagram shows a sector OACB of a circle with centre O. The point C is the midpoint of the arc AB.The diagram also shows a hollow cone with vertex O. The cone is formed by joining OA and OB.The cone has volume 56.8 cm3 and height 3.6 cm.Calculate the size of angle AOB of sector OACB. Give your answer correct to 3 significant figures. You must show all your working. ........................................................... °?(Total for question = 5 marks)?Q11.?The diagram shows a prism.The area of the cross section of the prism is 30 cm2. The length of the prism is 25 cm.Work out the volume of the prism. ........................................................... ?(Total for question = 3 marks)?Q12.?Here is the cross section of a steel girder.The cross section has two lines of symmetry.The girder is a prism.The length of the girder is 200 cm.Work out the volume of the girder............................................................ cm3(Total for Question is 5 marks)Q13.The diagram shows an L-shaped prism.Calculate the volume of the prism.?????????. . . . . . . . . . . . . . . . . . cm3(Total for Question is 3 marks)Q14.The diagram represents a shed.The shed is in the shape of a prism. The cross section of the prism is a hexagon. The hexagon has one line of symmetry. The walls of the shed are vertical. Calculate the volume of the shed.?????. . . . . . . . . . . . . . . . . . . . . .m3(Total for Question is 4 marks)Q15.?The diagram shows a prism.All the corners are right angles.Work out the volume of the prism............................................................? (Total for question = 4 marks)Q16.?A factory makes ice cream tubs in two sizes, small and large.The tubs are similar in shape.The height of the small tub is 5 cmThe volume of the small tub is 150 cm3The volume of the large tub is 500 cm3Work out the height of the large tub. Give your answer correct to 3 significant figures. ........................................................... cm?(Total for question = 2 marks)?Q17.?The diagram shows a solid metal cuboid.The areas of three of the faces are marked on the diagram. The lengths, in cm, of the edges of the cuboid are whole numbers.The metal cuboid is melted and made into cubes. Each of the cubes has sides of length 2.5 cm.Work out the greatest number of these cubes that can be made. ........................................................... ?(Total for question = 5 marks)?Q18.?Here is a frustum of a cone.The diagram shows that the frustum is made by removing a cone with height 3.2 cm from a solid cone with height 6.4 cm and base diameter 7.2 cm.The frustum is joined to a solid hemisphere of diameter 7.2 cm to form the solid S shown below.The density of the frustum is 2.4 g/cm3The density of the hemisphere is 4.8 g/cm3Calculate the average density of solid S. ........................................................... g/cm3?(Total for question = 5 marks)?Q19.?The diagram shows a hemisphere with diameter 8.4 cm.Work out the volume of the hemisphere. Give your answer correct to 3 significant figures. ........................................................... cm3?(Total for question = 2 marks)?Q20.?The diagram shows a solid shape. The shape is a cone on top of a hemisphere.The height of the cone is 10 cm. The base of the cone has a diameter of 6 cm. The hemisphere has a diameter of 6 cm.The total volume of the shape is kπ cm3, where k is an integer.Work out the value of k.k = ........................................................... ?(Total for question = 4 marks)?Q21.A water trough is in the shape of a prism.Hamish fills the trough completely.Water leaks from the bottom of the trough at a constant rate.2 hours later, the level of the water has fallen by 20 cm.Water continues to leak from the trough at the same rate.How many more minutes will it take for the trough to empty completely???????????????. . . . . . . . . . . . . . . . . . . . . . minutes(Total for Question is 6 marks)Q22.Here is a vase in the shape of a cylinder.??The vase has a radius of 5 cm. There are 1000 cm3 of water in the vase. Work out the depth of the water in the vase. Give your answer correct to 1 decimal place.????????..............................................................................................................................................(Total for Question is 3 marks)Q23.Ella is designing a glass in the shape of a cylinder.The glass must hold a minimum of ? litre of liquid.The glass must have a diameter of 8 cm.Calculate the minimum height of the glass. ?????????????..............................................................................................................................................(Total for Question is 5 marks)Q24.?* The diagram shows a solid wooden sphere.The radius of the sphere is 2 cm. The mass of the sphere is 45 grams.Wood will float on the Dead Sea only when the density of the wood is less than 1.24 g/cm3.Will this wooden sphere float on the Dead Sea?(Total for Question is 4 marks)Q25.?The diagram shows a metal rod, AB, resting inside a cylindrical tin.The tin is on a horizontal table. AC is a diameter of the base of the tin. B is on the top edge of the tin. BC is vertical.The radius of the base of the tin is 5 cm. The volume of the tin is 1178 cm3Find the angle between the rod and the base of the tin. Give your answer correct to the nearest degree. ........................................................... °?(Total for question = 4 marks)?Q26.?A hollow cylinder has radius r cm and height 6r cm. 3 spheres, also of radius r cm, are put into the cylinder.(a)??Work out the proportion of the cylinder that is not filled by the spheres. ........................................................... (3)The height of the cylinder is increased by 2r cm. Another sphere of radius r cm is put into the cylinder.Malcolm says,"There is no change in the proportion of the cylinder not filled by the spheres."(b)??Is Malcolm correct?Justify your answer. ............................................................................................................................................. ............................................................................................................................................. (1)?(Total for question = 4 marks)?Q27.?The diagram shows a container for grain.The container is a cylinder on top of a cone. The cylinder has a radius of 3m and a height of hm. The cone has a base radius of 3m and a vertical height of 4m.The container is empty. The container is then filled with grain at a constant rate.After 5 hours the depth of the grain is 6 metres above the vertex of the cone. After 9 hours the container is full of grain.Work out the value of h. Give your answer as a fraction in its simplest form. You must show all your working............................................................? (Total for question = 5 marks)Q28.Jane has a carton of orange juice.The carton is in the shape of a cuboid.? Diagram NOT accurately drawnThe depth of the orange juice in the carton is 8 cm.Jane closes the carton.Then she turns the carton over so that it stands on the shaded face.Work out the depth, in cm, of the orange juice now.?????????? . . . . . . . . . . . . . . . . . . . . . . cm(Total for Question is 3 marks)Q29.Terry fills a carton with boxes. Each box is a cube of side 10 cm. The carton is a cuboid with length ???60 cm width ???50 cm height ???30 cmWork out the number of boxes Terry needs to fill one carton completely.???????????..............................................................................................................................................(Total for Question is 3 marks)Q30.?The diagram shows a container used to store oil.The container is in the shape of a cylinder of radius 40 cm.The height of the oil in the container is 90 cm.65 litres of oil are taken from the container. 1 litre = 1000 cm3.Work out the new height of the oil in the container. Give your answer correct to one decimal place...........................cm(Total for Question is 4 marks)Q31.?Ali has some packets.Each packet has dimensions 40 cm by 8 cm by 50 cm.Ali fills a container with these packets. The container is a cube of side 2 m.Ali fills the container completely with these packets.Work out the number of packets............................................................(Total for Question is 4 marks)Q32.?The diagram shows a solid metal cylinder.The cylinder has base radius 3x cm and height h cm.The metal cylinder is melted. All the metal is then used to make 270 spheres.Each sphere has a radius of x cm.Find an expression, in its simplest form, for h in terms of x. ........................................................... ?(Total for question = 3 marks)?Q33.?* The diagram shows a swimming pool in the shape of a prism.The swimming pool is empty.Water from 3 water tankers is going to be put into the pool. There are 20 000 litres of water in each water tanker.Sam thinks that the surface of the water in the pool will be 10 cm below the top of the pool.Is Sam correct? You must show how you get your answer. (1 m3 = 1000 litres)?(Total for question = 5 marks)?Q34.?The diagram shows a solid cone.The diameter of the base of the cone is 24x cm. The height of the cone is 16x cm.The curved surface area of the cone is 2160π cm2. The volume of the cone is Vπ cm3, where V is an integer.Find the value of V............................................................?(Total for question is 5 marks)Q35.?*The diagram shows a container for oil. The container is in the shape of a cuboid. The container is empty.Sally has to fill the container with oil. A bottle of oil costs ?3.50 There are 3000 cm3 of oil in each bottle.Sally must not spend more than ?60 buying the oil.Can Sally buy enough oil to fill the container? You must show all your working.?(Total for question = 4 marks)?Q36.?The diagram shows a swimming pool in the shape of a prism.The swimming pool is empty.The swimming pool is filled with water at a constant rate of 50 litres per minute.(a) ?Work out how long it will take for the swimming pool to be completely full of water. Give your answer in hours. (1 m3 = 1000 litres)........................................................... hours(5)Here are four graphs.(b) ?Write down the letter of the graph that best shows how the depth of the water in the pool above the line MN changes with time as the pool is filled............................................................(1)? (Total for question = 6 marks)Q37.The diagram shows a large tin of pet food in the shape of a cylinder.The large tin has a radius of 6.5 cm and a height of 11.5 cm.A pet food company wants to make a new size of tin.The new tin will have a radius of 5.8 cm.It will have the same volume as the large tin.Calculate the height of the new tin.Give your answer correct to one decimal place............................................................ cm(Total for Question is 3 marks)Q38.?*Chao transports microwave ovens from China to the UK.He puts each microwave oven in a box. Each box is a cube of side 50cm.He then puts each box in a container. Each container is a cuboid of size 5m by 2.5m by 2m.Chao has 500 boxes. He has 3 containers.Will the 500 boxes fit into these 3 containers??(Total for question = 4 marks)?Q39.Sumeet has a pond in the shape of a prism.The pond is completely full of water. Sumeet wants to empty the pond so he can clean it. Sumeet uses a pump to empty the pond. The volume of water in the pond decreases at a constant rate. The level of the water in the pond goes down by 20 cm in the first 30 minutes.Work out how much more time Sumeet has to wait for the pump to empty the pond completely.? ???????????..............................................................................................................................................(Total for Question is 6 marks)Q40.?* Anne wants to fill 12 hanging baskets with compost.Each hanging basket is a hemisphere of diameter 40 cm.Anne has 4 bags of compost. There are 50 litres of compost in each bag.Has Anne got enough compost to fill the 12 hanging baskets??(Total for question = 4 marks)?Q41.?The diagram shows Helen's fish tank. The fish tank is in the shape of a cuboid.All the dimensions are correct to the nearest centimetre.Helen is going to use a bucket to fill the fish tank completely with water. There are 14 litres, correct to the nearest litre, of water in a full bucket.Will 25 full buckets of water definitely fill the fish tank? Justify your answer.?(Total for question = 4 marks)?Q42.?The diagram shows a swimming pool. The swimming pool is in the shape of a prism. The swimming pool is filled with water at a rate of 5 litres per second.Jeremy has 10 hours to fill the swimming pool. 1 m3 = 1000 litres.Will he completely fill the swimming pool in 10 hours? You must show all your working.?(Total for question = 5 marks)?Q43.?The diagram shows an oil tank in the shape of a prism. The cross section of the prism is a trapezium.The tank is empty.Oil flows into the tank. After one minute there are 300 litres of oil in the tank.Assume that oil continues to flow into the tank at this rate.(a)??Work out how many more minutes it takes for the tank to be 85 full of oil. ???????(1 m3 = 1000 litres)........................................................... minutes(5)The assumption about the rate of flow of the oil could be wrong.(b)??Explain how this could affect your answer to part (a). ............................................................................................................................................. ............................................................................................................................................. (1)? (Total for question = 6 marks)Q44.?Here is a cuboid.All measurements are in centimetres. x is an integer. The total volume of the cuboid is less than 900 cm3Show that x 5.? (Total for question = 3 marks)Q45.?A solid is made by putting a hemisphere on top of a cone.The total height of the solid is 5xThe radius of the base of the cone is xThe radius of the hemisphere is xA cylinder has the same volume as the solid. The cylinder has radius 2x and height hAll measurements are in centimetres.Find a formula for h in terms of xGive your answer in its simplest form............................................................? (Total for question = 5 marks)Q46.*? Marc drives a truck.The truck pulls a container.The container is a cuboid 10 m by 4 m by 5 m.Marc fills the container with boxes.Each box is a cuboid 50 cm by 40 cm by 20 cm.Show that Marc can put no more than 5000 boxes into the container.????????(Total for Question is 4 marks)Q47.?The diagram shows a sand pit. The sand pit is in the shape of a cuboid.Sally wants to fill the sand pit with sand. A bag of sand costs ?2.50 There are 8 litres of sand in each bag.Sally says,"The sand will cost less than ?70"Show that Sally is wrong.?(Total for question is 5 marks)Q48.?The diagram shows a metal bar in the shape of a prism.The length of the metal bar is 120 cm. The cross section of the metal bar is shown below.All corners are right angles.The metal bar is made from steel with density 8 g/cm3.Sean has a trolley. The trolley can carry a maximum mass of 250kg.How many metal bars can the trolley carry at the same time? You must show your working. ........................................................... ?(Total for question = 5 marks)?Q49.?The diagram shows a cuboid ABCDEFGH.AB = 7 cm, AF = 5 cm and FC = 15 cm.Calculate the volume of the cuboid. Give your answer correct to 3 significant figures............................................................ cm3?(Total for question is 4 marks)Q50.?Liquid A and liquid B are mixed together in the ratio 2 : 13 by volume to make liquid C.Liquid A has density 1.21 g/cm3Liquid B has density 1.02 g/cm3A cylindrical container is filled completely with liquid C. The cylinder has radius 3 cm and height 25 cm.Work out the mass of the liquid in the container. Give your answer correct to 3 significant figures. You must show all your working. ........................................................... g?(Total for question = 4 marks)?Q51.The diagram shows a pyramid.BCDE is a square with sides of length 10 cm. The other faces of the pyramid are equilateral triangles with sides of length 10 cm.(a) Calculate the volume of the pyramid. ?????Give your answer correct to 3 significant figures.??????. . . . . . . . . . . . . . . . . . . . . . . . cm3(4)(b) Find the size of angle DAB.???????????..............................................................................................................................................(2)(Total for Question is 6 marks)Q52.?The diagram shows a triangular prism.Work out the volume of the prism............................................................? (Total for question = 3 marks)Q53.Here is a solid prism.Work out the volume of the prism.????????. . . . . . . . . . . . . . . . . .cm3(Total for Question is 3 marks)Q54.?Here is a triangular prism.Work out the volume of this triangular prism............................................................(Total for Question is 4 marks)Q55.The diagram shows a prism.Work out the volume of the prism.???????????...........................................................cm3(Total for Question is 3 marks)Q56.A frustrum is made by removing a small cone from a similar large cone.The height of the small cone is 20 cm. The height of the large cone is 40 cm. The diameter of the base of the large cone is 30 cm.Work out the volume of the frustrum. Give your answer correct to 3 significant figures.?????? . . . . . . . . . . . . . . . . . . . . . . . .cm3(Total for Question is 4 marks)Q57.?The diagram shows a solid shape.The solid shape is made from a hemisphere and a cone. The radius of the hemisphere is equal to the radius of the base of the cone. The cone has a height of 10 cm. The volume of the cone is 270π cm3. Work out the total volume of the solid shape. Give your answer in terms of π............................................................ cm3?(Total for question = 5 marks)?Q58.?The diagram shows the area of each of three faces of a cuboid.The length of each edge of the cuboid is a whole number of centimetres.Work out the volume of the cuboid............................................................?(Total for question = 4 marks)?Q59.Work out the volume of the triangular prism.?????. . . . . . . . . . . . . . . . . . . . . . cm3(Total for Question is 2 marks)Q60.?The diagram shows a prism.All the corners are right angles.Work out the volume of the prism............................................................cm3?(Total for question = 3 marks)?Q61.?Here is a solid prism.Work out the volume of the prism. You must show all your working. ........................................................... cm3?(Total for question = 4 marks)?Q62.?Here is a prism.Work out the volume of the prism............................................................cm3?(Total for question = 4 marks)?Q63.?The diagram shows a sphere and a solid cylinder.The sphere has radius 6 cm. The solid cylinder has a base radius of 3 cm and a height of h cm.The total surface area of the cylinder is twice the total surface area of the sphere.Work out the ratio of the volume of the sphere to the volume of the cylinder. Give your answer in its simplest form. You must show all your working. ........................................................... ?(Total for question = 5 marks)?Q64.?A frustum is made by removing a small cone from a large cone as shown in the diagram.The frustum is made from glass. The glass has a density of 2.5 g / cm3Work out the mass of the frustum. Give your answer to an appropriate degree of accuracy............................................................ g? (Total for question = 5 marks)Q65.The diagram shows a solid triangular prism.The prism is made from metal. The density of the metal is 6.6 grams per cm3.Calculate the mass of the prism.??????????????..............................................................................................................................................(Total for Question is 3 marks)Q66.?The diagram shows a prism.All measurements are in centimetres. All corners are right angles.Find an expression, in terms of x, for the volume, in cm3, of the prism. You must show your working. Give your answer in its simplest form. ........................................................... ?(Total for question = 4 marks)?Q67.?A cone has a volume of 98 cm3. The radius of the cone is 5.13 cm.(a)?? Work out an estimate for the height of the cone. ........................................................... cm(3)John uses a calculator to work out the height of the cone to 2 decimal places.(b)?? Will your estimate be more than John's answer or less than John's answer?Give reasons for your answer. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. (1)?(Total for question = 4 marks)?Q68.The diagram shows a solid triangular prism. All the measurements are in centimetres.The volume of the prism is V cm3.Find a formula for V in terms of x. Give your answer in simplified form. ???????????????????..............................................................................................................................................(Total for Question is 3 marks)Q69.?A container is in the shape of a cuboid.The container is full of water.A cup holds 275 ml of water.What is the greatest number of cups that can be completely filled with water from the container? ........................................................... ?(Total for question = 4 marks)? ................
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