Loudoun County Public Schools



Study GuideSurface Area & VolumeSOL 7.5What do I need to know for the upcoming assessment?Calculate surface area and volume for a given rectangular prism or cylinder;Find a missing sides when given 2 dimensions and either volume or surface area;Solve practical problems involving surface area and volume; andUnderstand how scale factors affect the surface area and volume of rectangular prisms.Will I be able to use a calculator or formula sheet?Yes! You will be given both a calculator and a formula sheet during the assessment.What can I do to prepare for the assessment?Review your class notes, independent practice, and homework assignments;Finish any unfinished work from the unit;ASK questions BEFORE the assessment;Complete the attached practice; and Practice using IXL, 7th grade:P.28:Surface AreaP.29:VolumeP.30:Changes in scaleM6/7: Surface Area and Volume Study GuideDirections:Find the volume and surface area of each shape shown below. Show ALL work and round nearest hundredth. Make sure to include unit of measurement.342900124460007772401079500Volume84.00m3SA120.00m2Volume628.00in 3SA408.20in25715001790700077724017907000Volume240in3SA236in2Volume648.10ft3SA424.53ft2 Directions: Solve each problem and be sure to show ALL work. Round to the nearest hundredth if necessary.5) David and Vanessa built a recycling bin that is 6 ft wide, 12 ft long, and 14 ft tall. How much recycling will it hold?1008 ft36) The cylindrical canister of a fire extinguisher has a radius of 4 in and is 12 in tall. How many cubic inches can it hold?602.88in37) A soup can has a diameter of 8 cm and a height of 10.5 cm. How much metal is needed to make the can?364.24cm28) Lauren is wrapping a box that is 5 inches on all sides. How much paper will she need to cover the box?150in29) A water tank is 12 feet tall and has a diameter of 45 feet. How much water does the tank hold?847.80ft310) A swimming pool is 6 feet deep and has a diameter of 15 feet. How much water will it hold?1059.75ft311) Alex is building a sand box that is 6 feet wide, 3 feet long, and 15 inches high. How much sand will it hold?270ft312) Cesar is building a rectangular planter box that is open on the top. The planter will be 7 inches wide, 16 inches long, and 10 inches tall. How much wood will he need to make the planter box?572in213) A rectangular prism has a volume of 300 cm2. If the scale factor of a second rectangular prism is 3.5, what is the volume of the second rectangular prism?1050cm314) Harry has two cube-shaped boxes. The smaller box has an edge of 5 inches. The edges of the larger box are twice those of the small box. How does the volume of the larger box compare to the volume of the smaller box?The smaller box is 8 times smaller than the larger box.15) If the height of a rectangular prism is multiplied by a scale factor of 12, which of the following is true?ANSWER: C47339241517656858000151130473392515176462198251517654095750151765The surface area has increased by 2 square feet40957503238535718751066806 ft06 ftThe surface area is ? the size.The surface area has decreased by 60 square feet472376515176562103001517654095750151765The surface area is 2 times as large.6477000323852 ft2 ft46482001466858 ft8 ft16) If the height of a rectangular prism is multiplied by a scale factor of 3, which of the following is true?4495800-152405476875-158754991100-1333504990465-152405972175-133350The surface area increased by 324 square feet.44958006540406096000196859 ft9 ftThe surface area has increased by 3 square feet.The surface area is 3 times the size.499046510350544958001041405476875104140The surface area has increased by 1,584 square feet.585787519056 ft6 ft4800600863603 ft3 ftANSWER: A17) The width of the rectangular prism is doubled, which of the following is true? ANSWER D486727514859013 ft013 ft62007751454150415290014541503543300140335415290014478005581650140335The volume increases by 7,007.62769757429611 ft0011 ft3533775-1143000The volume is twice as small.The volume is 14 times as large.3600450812807 ft007 ft35433001644654162425160020005581650164465The volume is twice as large.18) The width of the rectangular prism is multiplied by a scale factor of 14 which of the following is true?ANSWER: A52101751015994162425101600369570010160000474345010160000369570015811500The volume will be 4 times smaller530542512763532 cm32 cmThe volume will decrease by 12.The volume will be half the size.474345014478000The volume 4 times larger.51339751371604 cm004 cm38671504699016 cm016 cm19) The rectangular below has volume of 672 in3, with a length 12 inches and width of 7 inches. What is the height? ANSWER B933450148907512 in012 in234315012446007 in7 in2419350654050h0h241935020637593345020637593345020637593345011017252019300110172553340011017252019300206375533400206375533400473075 a) The height is 16 inches. b) The height is 8 inches. c) The height is 10 inches d) The height is 19 inches 20) If the volume of a new rectangular prism can be represented by the formula V = 6lwh, what scale factor has one of the attributes of the original rectangular prism been multiplied by?6 TIMES21) If the surface area of a rectangular prism can be represented by the formula, SA = 2lw+ 8lh + 8wh, what scale factor has the height of the original rectangular prism been multiplied by?THE SCALE FACTOR IS 4. ................
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