Study Guide Surface Area & Volume SOL 7.5

Transcription

1 Study Guide Surface Area & Volume SOL 7.5 What 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; and Understand 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, 7 th grade: o X.28: Surface Area o X.29: Volume o X.30: Changes in scale SG M6/7: Surface Area & Volume Page 1

2 M6/7: Surface Area and Volume Study Guide Directions: 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. 1) 2) Volume SA Volume SA Directions: Solve each problem and be sure to show ALL work. Round to the nearest hundredth if necessary. 3) 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? 4) 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? 5) 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? 6) Lauren is wrapping a box that is 5 inches on all sides. How much paper will she need to cover the box? SG M6/7: Surface Area & Volume Page 2

3 7) A water tank is 12 feet tall and has a diameter of 45 feet. How much water does the tank hold? 8) A swimming pool is 6 feet deep and has a diameter of 15 feet. What is the size of pool liner needed for the sides and bottom of the pool? 9) Alex is building a sand box that is 6 feet wide, 3 feet long, and 15 inches high. How much sand will it hold? 10) 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? 11) A rectangular prism has a volume of 300 cm 3. If the scale factor of a second rectangular prism is 3.5, what is the volume of the second rectangular prism? 12) 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? 13) If the height of a rectangular prism is multiplied by a scale factor of 1, which of the following is true? 2 a) The surface area has increased by 2 square feet b) The surface area is ½ the size. c) The surface area has decreased by 60 feet 6 ft d) The surface area is 2 times as large. 8 ft 2 ft SG M6/7: Surface Area & Volume Page 3

4 14) If the height of a rectangular prism is multiplied by a scale factor of 3, which of the following is true? a) The surface area increased by 324 square feet. b) The surface area has increased by 3 square feet. 9 ft c) The surface area is 3 times the size. d) The surface area has increased by 1,584 square feet. 3 ft 6 ft 15) The width of the rectangular prism is doubled, which of the following is true? a) The volume increases by 7, ft b) The volume is twice as small. c) The volume is 14 times as large. 11 ft d) The volume is twice as large. 7 ft 16) The width of the rectangular prism is multiplied by a scale factor of 1 which of the following is true? 4 a) The volume will be 4 times smaller b) The volume will decrease by cm c) The volume will be half the size. d) The volume will be 4 times larger. 16 cm 4 cm SG M6/7: Surface Area & Volume Page 4

5 17) The rectangular below has volume of 672 iiii 3, with a length 12 inches and width of 7 inches. What is the height? a) The height is 16 inches. b) The height is 8 inches. 12 in h 7 in c) The height is 10 inches d) The height is 19 inches 18) 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? 19) 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? 20) A pencil box has a base area of 15 square inches and a height of 2 inches. If the length and width of the box is longer than 2 inches, what is the surface area of the box? SG M6/7: Surface Area & Volume Page 5

6 Answer Key 1) V=84 m 3 SA=122 m 2 2) V=628 in 3 SA=408.2 in 2 3) V=1,008 ft 3 4) V= in 3 5) SA= cm 2 6) SA=150 in 2 7) V=19,075 ft 3 8) SA= ft 2 9) V=270 ft 3 10) SA=572 in 2 11) V=1,050 cm 3 12) The larger box has a volume that is 8 times greater than the small box. 13) C 14) A 15) D 16) A 17) B 18) The scale factor is 6. 19) The scale factor of the height is 4. 20) SA=62 inches 2 SG M6/7: Surface Area & Volume Page 6