Surface Area and Volume Unit Test

1. Use Euler's formula to find the missing number. Vertices: 13 Edges: 28 Faces: ?

Answer: A) 17

2. Describe the cross section. (Picture of a cube and a shaded trapezoid in the middle)

Answer: B) Trapezoid

3. A department store sells small boxes in which customers can store potpourri. The diagram below shows one of the boxes. The diagram is not drawn to scale. (Picture of a rectangular prism 3.12cm, 17cm, 5cm) What are the lateral area and the surface area of the box to the nearest whole number? Use the large 17cm x 5cm rectangles on the top and bottom as the bases.

Answer: C) 137cm^2;307cm^2

4. Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. The figure is not drawn to scale. (3m, 9m, 37, 9.49m)

Answer: C) 795m^2;822m^2

5. Find the surface area of the cylinder to the nearest whole number. The figure is not drawn to scale. (12in, 17in)

Answer: C) 2,187in^2

6. Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale. (12m, 6 square root 3, 11m)

Answer: B) 770m^2

7. The lateral area of a cone is 574pi cm^2. The radius is 19.6cm. What is the slant height to the nearest tenth of a centimeter?

Answer: B) 29.9cm

8. What are the lateral area and the surface area of the cone shown below? Round the answers to the nearest tenth. The figure is not drawn to scale. (14ft, 27ft)

Answer: C) LA=1,187.5 ft^2; SA = 1,803.3 ft^2

9. What is the volume of the given prism? Round the answer to the nearest tenth of a centimeter. The figure is not drawn to scale. (8.8cm, 4.7cm, 13.1cm)

Answer: C) 541.8cm^3

10) Find the volume of the cylinder in terms of pi. The diagrams are not drawn to scale. (11m, 1.9m)

Answer: D) 39.71pi m^3

11) What is the height of the cylinder? The figure is not drawn to scale. (V=323.5in^3, 7in)

Answer: C) 2.1in

12) Find the volume of the square pyramid shown. Round to the nearest whole number. The diagrams are not drawn to scale. (11cm, 12cm, 12cm)

Answer: 528cm^3

13) A rectangular pyramid fits exactly on top of a rectangular prism. the prism has a length of 18cm, a width of 6cm, and a height of 9cm. The pyramid has a height of 15cm. Find the volume of the composite space figure.

Answer: 1,512cm^3

14) A spherical balloon has a circumference of 21 cm. What is the approximate surface area of the balloon to the nearest square centimeter?

Answer: 140cm^2

15) What is the volume of the sphere? Round the answer to the nearest cubic unit. (18cm)

Answer: 3,054cm^3

16) The volume of a sphere is 3,000pi m^3. What's the surface area fo the sphere to the nearest square meter?

Answer: C) 2,158m^2

17) Determine whether the two figures are similar. If so, give the similarity ratio fo the smaller figure to the larger figure. The figures are not drawn to scale. (Left, smaller rectangular prism(3, 4, 14) Right, larger rectangular prism(24, 32, 112))

Answer: C) yes; 1:8

18) The volumes of two similar solids are 1,331 m^3 and 216 m^3. the surface area of the larger solid is 484m^2. What's the surface area of the smaller solid?

Answer: C) 144m^2

19. What's the lateral area of the cone to the nearest whole number. The figure is not drawn to scale. (Cone with 40m, 60m)

Answer: 4,712m^2

20. What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 24 cm?

Answer: 4,608cm^3

The questions are different for everyone so take what you need. Good luck to everyone!