There are two pipes A and B. If ‘A’ fills 10 liters in ...



. Smita made a cube of size 5*5*5 by using smaller cubes of 1*1*1. She created solid larger cube then she decided to make a hollow cube of the same size, can you find out how many 1*1*1 cubes will she require make hollow larger cube?5^3-3^3 = 125 -27 = 98 cubes are required.There are two pipes A and B. If ?€?A?€? fills 10 liters in an hour B can fills 20 liters in same time. Likewise B can fill 10, 20, 40, 80,160?€?.if B filled in (1/16)th of a tank in 3 hours, how much time will it take to fill completely?1/16 --- 3 hours?1/8 ---- 4 hrs1/4 --- 5 hrs1/2 --- 6 hrs1 --- 7 hrs..so ans is in 7 hrs...Two pipes can fill a tank in 4 hr and 5 hr respectively. If they are turned on alternatively for 1 hr each, the tank will be filled in1st tank = 1/4 tank per hour, 2nd tank = 1/5 tank/ hourafter 2 hours = 1/4 + 1/5 = 9/20, After 4 hrs = 9/10.in 5th hour 1st pipe's turn. remaining = 1/101st tank will take 240/10 = 24 mins to fill the remaining.So total 4 hrs 24 mins.A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole icecream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice-cream cone.radius =3cmvolume of given ice cream =(pie)*6?*15=540(pie)dividing to 10 children volume given to a child =54(pie)let r be radius and h be the height of the cone,then(pie)r?h/3 + 2(pie)r?/3=54(pie)also given h=4r4r?/3 +2r?/3=542r?=54r?=27 r=3Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row of two balls and so on. If 669 more balls are added, then all the balls can be arranged in the shape of a square and each of the sides then contains 8 balls less than each side of thetriangle did. The initial number of balls isAnswer 1540suppose there n rows in equilateral triangle .then no.of balls=n(n+1)/2now 669 more balls are added and forms a square with sides of n-8 balls.therefore 669+n(n+1/2=(n-8)?simplifying we get n?-33n-1210=0n=55therefore no.of balls = 55*56/2=1540actually we are finding a triangular no. which is 669 less than a perfect square.(1540+669=2209,which is a perfect square)All faces of a cube with 8m edge are painted red.if cube is cut into smaller cubes of 2m edge,how many of the 2m edge have paint on exactly on one face?a)24b)36c)60d)48A cuboid of length 4 cm,breadth 6 cm and height 8 cm is formed using units cubes.All the faces of the cuboid are painted using different colours.now the cubes are seperated and the cubes with no face painted are used to form a new cuboid.Find the volume of a new formed cuboid.volume of it =4*6*8=192unit cubes are used,so no. of cubes=192/(1*1*1)=192 no. of cubes.now there are 8 layers of cuboid of its lenght=4cm and breadth=6cmhence all the faces of cuboid are painted using diffrent coliurs ,so no of cubes with no face painted--in 1st layer=0in 2nd layer to 7th layer=6*8=48in 8th or last layer=0so total no of cubes with no face painted =48so the volume of new formed cuboid is 48 cm^3OR48cc.unit cubes at the edges are chopped off.length, breadth and height are reduced by 2 units (1 at each of the ends)therefore volume of the new cube=2*4*6=48all faces of a cube witwh an 8m edge are painted red. if the cube is cut in to smaller cube with a 2m edge how many of the 2 m cubes have painted on exactly one facea)24 b)36 c)60 D)48clearly there will be 16 coloumns of 4 cube each formed after cutting the 8m cube into 2m cube.there are 8 cube in layer1,8 cube in layer 2 and 8 cube in layer3 and 4 cube in layer 4 which has one sided paintedso total is 4+8+8+8=24 cubes(ans)short formula for find one side painted cube is6(n-2)^2=6[(4-2)]^2=6*4=24 cubes(ans)here we take n=4,because if we cut 8m cube into 2m cube,then there will 4 cubes produceda boy wants to make cuboids of dimensions 5m,6m,7m from small cubes of .03m 3.later he realizes he can make same cuboids by making it hollow.then it takes some cubes less.what is the number of the cubes to be removed?volume of the small cube = 0.03 m^3so side of this cube = cubic root of 0.03 m^3 = .312 mso after removing the outermost layer the dimensions for the inner cuboid will be (5-2*0.312), (6-2*0.312), (7-2*0.312)so total volume will be (4.376)*(5.376)*(6.376) = 150 m^3so no of cubes will be 150/0.03 = 5000so we can remove 5000 inner cubes?Anita make cube with dimension 5*5*5 using 1*1*1 cubes.find no. Of cubes to make it hollow of same shape.To make the 5*5*5 hollow, the inner cubic part must be removed. This would constitute one cube each from front,back,top,bottom,left and right ! Since the 5*5*5 is made up of 1*1*1 cubes, 3*3*3 cubes (i.e. 5-2*5-2*5-2) would have to be removed to make it hollow with the shape retained. 27 cubes would be removed, remaining 125-27=98.A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?Side of cube = 5 cm and its thickness = 1 cmso volume of outer cube = 5*5*5 volume of inner cube = 3*3*3 (as 1cm is taken off at both ends)volume of the hollow cube = 5*5*5 - 3*3*3 = 125-27 = 98So total no of small cubes of the size 1 cm = 98/1*1*1 = 98we know a cube has 6 faces so total no of face = 98*6 = 588One surface of outer cube contains a total of 25 surface of smaller cube , so when 4 surfaces of outer cube is painted total no of surface of small cubes i.e supposed to be painted is 4*25 = 100So the total no of surfaces of small cube that will be remained unpainted is 588-100 = 488he length and breadth of a field is 300x400ft,if there are 3 ants on average per square inch of field,find the approximate number of ants in fieldArea = 300*12*400*12 sq inchesno of ants = 3600*4800*3= 108*48*10^4i.e……as 300 ft=3600 inch and 400 ft=4800 inch.then area in sqr inch=172800001 sqr inch need 3 ant hence 17280000 sqr inch need 3*17280000 ants.diagonal of a square is double the side of an equilateral triangle find the ratio of area of triangle to area of squarelet sides of equilateral triangle be 'a', therefore area= √3/4 * a^2now, diagonal of square is 2a therefore sides of square will be √2*aand area of square = 2 a^2hence, ratio = (√3/4* a^2)/(2* a^2)answer = √3/8Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side.?The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) isa)3 b)5 c) 2 d)1The meaning of this question is little complicated. In easy language the question should be:There are some points in the plane. We have to make a separation between these points by forming a line in such a way that one point could be separate from the others. No 3 points are in a line. Maximum no of methods for plotting the line and minimum no of methods for plotting the line will be (arrangement of points is your choice)Now Answer Is:For Maximize: The number of methods, Points should be drawn in the circumference of the CIRCLE So answer would be the number of total point in the plane.For minimize: The number of methods we should draw 3 points in a TRIANGLE and all other point inside this triangle in such a way that no 3 points could be in a line.If it will be allowed to draw the points in a line then minimum possibilities will be 2 only, because if we take all points in a line then you can separate only the corner points from the others.For exampleIf we have 10 points then maximum possibilities = 10and minimum = 3similarly for 5 points?Max = 5, Min = 3for 19?max= 19 Min = 3What is the distance between the z-intercept from x-intercept in the eqn ax+by+cz+d=0Distance between x-intercept and z-intercept is given by square root of (d/a)^2 + (d/c)^2Leena cuts small cubes of 3 cubic cm each.She joined it to make a cuboid of length 10 cm,width 3cm, and depth 3 cm.How many more cubes does she need to make a perfect cube? a)910 b)250 c)750 d)650there is a mistake in question,instead of 1 cubic cm, they have given 3 cubic cmso if Leena cuts small cubes of 1 cubic cm eachthen : [(10*10*10)-(10*3*3)]/1 = 910Q:- A boy wants to make cuboids of dimension 5m,6m & 7m from small cubes of .03m^3.Later he realized that he can make some cuboids by making it hollow.Then it takes some cubes less.What is the number of cubes to be removed a)2000 b)5000 c)3000 d)7000total no. of cubes needed to make cuboid from .03 cubes are (5*6*7)/.03=7000and no. of cubes needed to make it hollow is 5*6*7-(5-2)*(6-2)*(7-2)=150and total no. of cubes of .03 needed to make it hollow are 150/.03=5000so total no. of cubes to be removed are 7000-5000=2000so 2000 is the right ans.there r three buckets..of 8,5 n 3 litres...out of which only 8 ltr bucket is fully filled...u hv to fill exact 4-4 ltr liquid in 8 and 5 litre bucket by using only these buckets in minimm num of steps......8ltr 5ltr 3ltrinitially 8 0 0step1 3 5 0step2 3 2 3step3 6 2 0step4 6 0 2step5 1 5 2step 6 1 4 3step 7 4 4 0total 7 stepsIf a pipe can fill the tank within 6hrs.But due to leak it takes 30 min more.Now the tank is full then how much time will it take to empty the tank throught the leak.?a)78 b)56 c)66 d)5978 hourLet capacity be 6litresthen pipe takes 1litre/hourpipe/leak = 6/6.5 litre/hour(as they are inveresly proplational)so leak = 1/13 litre per hourfor 6 litres it will take 13*6 = 78 hour10. A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled completely or emptied completely as the case may be? .(A) Emptied; 16 mins (B) Filled; 8 mins (C) Emptied; 12 mins (D) Filled; 12 mins (E) None of Theseif A and B open togethersince B can empty faster than A so tank will empty not fill.the whole tank will empty in 16*8/(16-8) =16 minsince tank is half so it will take only 8 min to empty.Ans:EA cistern is two-third full of water. Pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes. Once the cistern is emptied, how much time will they take to fill it together completely?(A) 12 minutes (B) 12.5 min (C) 14.4 min (D) 10.2 min (E) 14.66 minto fill (1/3)rd A takes 12 minutes, To fill full tank 36 minutesto fill (1/3)rd B takes 8 minutes, To fill full tank 24 minutes(1/A)+(1/B)=(1/(A&B));A&B==>when both A and B are combined together to do the work==>(1/36)+(1/24)=(1/(A&B))A&B=(36*24)/(36+24)=14.4Fill dirt or fill soil is usually the sub-soil removed from an excavation side and is used to level a place or createartificial mounds. If the average density of sub?€”soil removed from a site is 3gm/cu cm and it weight 400 kg.How many hemispherical pits each of volume 240 cubic cm, can this sub-soil fill?(a)555 (b)277 (c)556 (d)5543gm per cm cube and there are hemispheric pits of capacity 240 cm cubeso..each hemisphere can contain 3*240=720cm cube soil..so total 0f 400kg i.e. 400*1000=4,00,000gms will be held in4,00,000/720=555.55 so approx 555 hemispheric pits are required...556 cannot be as 555.55 is less than 556..A hollow cube of size 5cm is taken,with a thickness of 1cm.It is made of smaller cubes of size 1cm.if 4 faces of the outer surface of the cube are painted,totally how many faces of the smaller cubes remain unpainted?(A)500 (B)800 (C)488 (D)9005^3-3^3=588-100=488A cistern is two third full of water.pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes. once the cistern is emptied, how much time will they take to fill it together completely?(A)12minutes (B)12.5min (C)14.4min (D)10.2min (E)14.66minfor A : 12 mint for one third of water filling?hence it takes 36 mint to fill it completelyfor B: 8 mint to fill one third of cisternhence it takes 24 mint to fill it completely.for A & B :1/t = 1/36 + 1/24hence t = 14.4 mint so, ans is CA hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?a) 800 b) 488 c) 900 d) 500(5*5*5)-(3*3*3)=9898*6=589588-(4*25)=488Ahollow cube of size 5 cm is taken with a thickness of 1 cm. it is made of smaller cubes of size 1 cm. if 3 faces of the outer surface of the cube are painted totally how many faces of the smaller cubes remain unpainted?525 900 825 513No. of small cubes required to make the bigger cube= (5*5*5-(5-2)*(5-2)*(5-2))/1*1*1 = 98Small cubes surfaces on one side of bigger cube= 5*5= 25Total no of sides of small cubes= 98*6 = 588?But 3 faces of the outer surface are painted i.e. 3*25= 75 surfaces of smaller cube are painted alreadySo remaining surfaces to be painted are= 588-75=513If a pipe can fill the tank within 6hrs.But due to leak it takes 30 min more. Now the tank is full then how much time will it take to empty the tank throught the leak?a) 78 b) 56 c) 66 d) 59let the flow of pipe is 1 lit/hrso in 6 hrs 6 lites water is filled which is the capacity of tank(6 lit.)it takes 0.5 hrs extra for leak.which means water is leaking at the rate 0.5 liter per 6.5 hrs (because in 6 hrs tank without leak will fill 6 lit of water and if leaking it will take 6.5 hrs so extra water filled in 0.5 hrs is half liter which is the compensation of leaking in 6.5 hrs)so 0.5 liters in 6.5 hrs leaking time required for 1 liter to leak is 13?therefore time required for 6 liters = 6*13=78[answer.]Totally 3 beakers A,B,C are present. A of capacity X lit, B of capacity 2X lit,C of capacity 3X lit. if A contain 2/3 of wine and rest with water. B contains 1/4 of wine and rest with water. if these two liquids are poured in to the 3rd beaker what is the proportion of wine in the 3rd beaker.A contains (2/3)*x lt.wine(7/6)*xB contains (1/4)*2x lt. wine and (3/4)*2x lt. waterif we mix both we will get 3x lts of solution and in thatwine=[(2/3)*x]+[(1/2)*x]=(7/6)*x ltso proportion of wine=(7/6)*x/3x=7/18....A circ ular cylinder can hold 61.6 cc of water. If t he height of the cylinder is 40 c m and theouter diameter is 16 mm, what is the thicknes s of t he mat erial of the c ylinder?(a) 0.2 mm (b) 0.3 mm (c) 1 mm (d) 2 mmcircular cylinder volume is given...61.6cc=pi*(inner radius)2*hnote all units in above equation are in centimetersnow solving the equation you get inner radius=0.7 cm=7mmthus thickness= (outer dia/2)-inner radius= 8-7=1 mm ................
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