Exercises: Solve Geometry Applications: Volume and Surface Area (6.4)

Exercises: Find Volume and Surface Area of Rectangular Solids

Instructions: For questions 1-4, find

a. the volume and
b. the surface area of the rectangular solid with the given dimensions.

1. length [latex]2[/latex] meters, width [latex]1.5[/latex] meters, height [latex]3[/latex] meters
Solution

a. [latex]9[/latex] cu. m
b. [latex]27[/latex] sq. m

2. length [latex]5[/latex] feet, width [latex]8[/latex] feet, height [latex]2.5[/latex] feet
3. length [latex]3.5[/latex] yards, width [latex]2.1[/latex] yards, height [latex]2.4[/latex] yards
Solution

a. [latex]17.64[/latex] cu. yd.
b. [latex]41.58[/latex] sq. yd.

4. length [latex]8.8[/latex] centimeters, width [latex]6.5[/latex] centimeters, height [latex]4.2[/latex] centimeters

Exercises: Find Volume and Surface Area of Rectangular Solids

Instructions: For questions 5-8, solve.

5. Moving van. A rectangular moving van has length [latex]16[/latex] feet, width [latex]8[/latex] feet, and height [latex]8[/latex] feet. Find its

a. volume and
b. surface area.

Solution

a. [latex]1\text{,}024[/latex] cu. ft
b. [latex]640[/latex] sq. ft

6. Gift box A rectangular gift box has length [latex]26[/latex] inches, width [latex]16[/latex] inches, and height [latex]4[/latex] inches. Find its

a. volume and
b. surface area.

7. Carton A rectangular carton has length [latex]21.3[/latex] cm, width [latex]24.2[/latex] cm, and height [latex]6.5[/latex] cm. Find its

a. volume and
b. surface area.

Solution

a. [latex]3\text{,}350.49[/latex] cu. cm
b. [latex]1\text{,}622.42[/latex] sq. cm

8. Shipping container A rectangular shipping container has length [latex]22.8[/latex] feet, width [latex]8.5[/latex] feet, and height [latex]8.2[/latex] feet. Find its

a. volume and
b. surface area.

Exercises: Find Volume and Surface Area of Rectangular Solids

Instructions: For questions 9-12, find

a. the volume and
b. the surface area of the cube with the given side length.

9. [latex]5[/latex] centimeters
Solution

a. [latex]125[/latex] cu. cm
b. [latex]150[/latex] sq. cm

10. [latex]6[/latex] inches
11. [latex]10.4[/latex] feet
Solution

a. [latex]1124.864[/latex] cu. ft.
b. [latex]648.96[/latex] sq. ft

12. [latex]12.5[/latex] meters

Exercises: Find Volume and Surface Area of Rectangular Solids

Instructions: For questions 13-16, solve.

13. Science center. Each side of the cube at the Discovery Science Center in Santa Ana is [latex]64[/latex] feet long. Find its

a. volume and
b. surface area.

Solution

a. [latex]262\text{,}144[/latex] cu. ft
b. [latex]24\text{,}576[/latex] sq. ft

14. Museum. A cube-shaped museum has sides [latex]45[/latex] meters long. Find its

a. volume and
b. surface area.

15. Base of statue. The base of a statue is a cube with sides [latex]2.8[/latex] meters long. Find its

a. volume and
b. surface area.

Solution

a. [latex]21.952[/latex] cu. m
b. [latex]47.04[/latex] sq. m

16. Tissue box. A box of tissues is a cube with sides 4.5 inches long. Find its

a. volume and
b. surface area.

Exercises: Find the Volume and Surface Area of Spheres

Instructions: For questions 17-20, find

a. the volume and
b. the surface area of the sphere with the given radius.

Round answers to the nearest hundredth.

17. [latex]3[/latex] centimeters
Solution

a. [latex]113.04[/latex] cu. cm
b. [latex]113.04[/latex] sq. cm

18. [latex]9[/latex] inches
19. [latex]7.5[/latex] feet
Solution

a. [latex]1\text{,}766.25[/latex] cu. ft
b. [latex]706.5[/latex] sq. ft

20. [latex]2.1[/latex] yards

Exercises: Find the Volume and Surface Area of Spheres

Instructions: For questions 21-24, solve. Round answers to the nearest hundredth.

21. Exercise ball. An exercise ball has a radius of [latex]15[/latex] inches. Find its

a. volume and
b. surface area.

Solution

a. [latex]14\text{,}130[/latex] cu. in.
b. [latex]2\text{,}826[/latex] sq. in.

22. Balloon ride. The Great Park Balloon is a big orange sphere with a radius of [latex]36[/latex] feet . Find its

a. volume and
b. surface area.

23. Golf ball. A golf ball has a radius of [latex]4.5[/latex] centimeters. Find its

a. volume and
b. surface area.

Solution

a. [latex]381.51[/latex] cu. cm
b. [latex]254.34[/latex] sq. cm

24. Baseball. A baseball has a radius of [latex]2.9[/latex] inches. Find its

a. volume and
b. surface area.

Exercises: Find the Volume and Surface Area of a Cylinder

Instructions: For questions 25-28, find

a. the volume and
b. the surface area of the cylinder with the given radius and height.

Round answers to the nearest hundredth.

25. radius [latex]3[/latex] feet, height [latex]9[/latex] feet
Solution

a. [latex]254.34[/latex] cu. ft
b.[latex]226.08[/latex] sq. ft

26. radius [latex]5[/latex] centimeters, height [latex]15[/latex] centimeters
27. radius [latex]1.5[/latex] meters, height [latex]4.2[/latex] meters
Solution

a. [latex]29.673[/latex] cu. m
b. [latex]53.694[/latex] sq. m

28. radius [latex]1.3[/latex] yards, height [latex]2.8[/latex] yards

Exercises: Find the Volume and Surface Area of a Cylinder

Instructions: For questions 29-32, solve. Round answers to the nearest hundredth.

29. Coffee. can A can of coffee has a radius of [latex]5[/latex] cm and a height of [latex]13[/latex] cm. Find its

a. volume and
b. surface area.

Solution

a. [latex]1\text{,}020.5[/latex] cu. cm
b. [latex]565.2[/latex] sq. cm

30. Snack. pack A snack pack of cookies is shaped like a cylinder with radius [latex]4[/latex] cm and height [latex]3[/latex] cm. Find its

a. volume and
b. surface area.

31. Barber shop pole. A cylindrical barber shop pole has a diameter of [latex]6[/latex] inches and height of [latex]24[/latex] inches. Find its

a. volume and
b. surface area.

Solution

a. [latex]678.24[/latex] cu. in.
b. [latex]508.68[/latex] sq. in.

32. Architecture. A cylindrical column has a diameter of [latex]8[/latex] feet and a height of [latex]28[/latex] feet. Find its

a. volume and
b. surface area.

Exercises: Find the Volume of Cones

Instructions: For questions 33-36, find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.
33. height [latex]9[/latex] feet and radius [latex]2[/latex] feet
Solution

[latex]37.68[/latex] cu. ft

34. height [latex]8[/latex] inches and radius [latex]6[/latex] inches
35. height [latex]12.4[/latex] centimeters and radius [latex]5[/latex] cm
Solution

[latex]324.47[/latex] cu. cm

36. height [latex]15.2[/latex] meters and radius [latex]4[/latex] meters

Exercises: Find the Volume of Cones

Instructions: For questions 37-40, solve. Round answers to the nearest hundredth.
37. Teepee. What is the volume of a cone-shaped teepee tent that is [latex]10[/latex] feet tall and [latex]10[/latex] feet across at the base?
Solution

[latex]261.67[/latex] cu. ft

38. Popcorn cup. What is the volume of a cone-shaped popcorn cup that is [latex]8[/latex] inches tall and [latex]6[/latex] inches across at the base?
39. Silo. What is the volume of a cone-shaped silo that is [latex]50[/latex] feet tall and [latex]70[/latex] feet across at the base?
Solution

[latex]64\text{,}108.33[/latex] cu. ft

40. Sand pile. What is the volume of a cone-shaped pile of sand that is [latex]12[/latex] meters tall and [latex]30[/latex] meters across at the base?

Exercises: Everyday Math

Instructions: For questions 41-42, answer the given everyday math word problems.

41. Street light post. The post of a street light is shaped like a truncated cone, as shown in the picture below. It is a large cone minus a smaller top cone. The large cone is [latex]30[/latex] feet tall with base radius [latex]1[/latex] foot. The smaller cone is [latex]10[/latex] feet tall with base radius of [latex]0.5[/latex] feet. To the nearest tenth,

a. find the volume of the large cone.
b. find the volume of the small cone.
c. find the volume of the post by subtracting the volume of the small cone from the volume of the large cone.

An image of a cone is shown. There is a dark dotted line at the top indicating a smaller cone.
Figure 6P.4.1
Solution

a. [latex]31.4[/latex] cu. ft
b. [latex]2.6[/latex] cu. ft
c. [latex]28.8[/latex] cu. ft

42. Ice cream cones A regular ice cream cone is 4 inches tall and has a diameter of [latex]2.5[/latex] inches. A waffle cone is [latex]7[/latex] inches tall and has a diameter of [latex]3.25[/latex] inches. To the nearest hundredth,

a. find the volume of the regular ice cream cone.
b. find the volume of the waffle cone.
c. how much more ice cream fits in the waffle cone compared to the regular cone?

Exercises: Writing Exercises

Instructions: For questions 43-44, answer the given writing exercises.
43. The formulas for the volume of a cylinder and a cone are similar. Explain how you can remember which formula goes with which shape.
Solution

Answers will vary.

44. Which has a larger volume, a cube of sides of [latex]8[/latex] feet or a sphere with a diameter of [latex]8[/latex] feet? Explain your reasoning.

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Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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