Volume and Surface Area of Solids

Description: This quiz is designed to assess your understanding of the concepts related to the volume and surface area of various solids, including cubes, spheres, cylinders, and cones.
Number of Questions: 15
Created by:
Tags: geometry volume surface area solids
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What is the volume of a cube with side length (s)?

  1. (s^2)

  2. (s^3)

  3. (2s^3)

  4. (4s^3)


Correct Option: B
Explanation:

The volume of a cube is given by (s^3), where (s) is the length of one side of the cube.

What is the surface area of a cube with side length (s)?

  1. (6s^2)

  2. (4s^2)

  3. (2s^2)

  4. (8s^2)


Correct Option: A
Explanation:

The surface area of a cube is given by (6s^2), where (s) is the length of one side of the cube.

What is the volume of a sphere with radius (r)?

  1. (\frac{4}{3}\pi r^3)

  2. (\frac{1}{3}\pi r^3)

  3. (\pi r^3)

  4. (2\pi r^3)


Correct Option: A
Explanation:

The volume of a sphere is given by (\frac{4}{3}\pi r^3), where (r) is the radius of the sphere.

What is the surface area of a sphere with radius (r)?

  1. (4\pi r^2)

  2. (2\pi r^2)

  3. (\pi r^2)

  4. (\frac{1}{2}\pi r^2)


Correct Option: A
Explanation:

The surface area of a sphere is given by (4\pi r^2), where (r) is the radius of the sphere.

What is the volume of a cylinder with radius (r) and height (h)?

  1. (\pi r^2 h)

  2. (2\pi r^2 h)

  3. (\frac{1}{2}\pi r^2 h)

  4. (4\pi r^2 h)


Correct Option: A
Explanation:

The volume of a cylinder is given by (\pi r^2 h), where (r) is the radius of the base and (h) is the height of the cylinder.

What is the surface area of a cylinder with radius (r) and height (h)?

  1. (2\pi r h + 2\pi r^2)

  2. (\pi r h + 2\pi r^2)

  3. (2\pi r h + \pi r^2)

  4. (\pi r h + \pi r^2)


Correct Option: A
Explanation:

The surface area of a cylinder is given by (2\pi r h + 2\pi r^2), where (r) is the radius of the base and (h) is the height of the cylinder.

What is the volume of a cone with radius (r) and height (h)?

  1. (\frac{1}{3}\pi r^2 h)

  2. (\frac{1}{2}\pi r^2 h)

  3. (\pi r^2 h)

  4. (2\pi r^2 h)


Correct Option: A
Explanation:

The volume of a cone is given by (\frac{1}{3}\pi r^2 h), where (r) is the radius of the base and (h) is the height of the cone.

What is the surface area of a cone with radius (r) and height (h)?

  1. (\pi r h + \pi r^2)

  2. (2\pi r h + \pi r^2)

  3. (\pi r h + 2\pi r^2)

  4. (2\pi r h + 2\pi r^2)


Correct Option: A
Explanation:

The surface area of a cone is given by (\pi r h + \pi r^2), where (r) is the radius of the base and (h) is the height of the cone.

A cube has a volume of (64) cubic centimeters. What is the length of one side of the cube?

  1. (2) cm

  2. (4) cm

  3. (6) cm

  4. (8) cm


Correct Option: B
Explanation:

Since the volume of a cube is (s^3), where (s) is the length of one side, we can solve for (s) by taking the cube root of the volume. (\sqrt[3]{64} = 4), so the length of one side of the cube is (4) cm.

A sphere has a radius of (5) centimeters. What is the volume of the sphere?

  1. (523.6) cm³

  2. (339.2) cm³

  3. (267.9) cm³

  4. (133.9) cm³


Correct Option: A
Explanation:

The volume of a sphere is given by (\frac{4}{3}\pi r^3). Substituting (r = 5) cm, we get (\frac{4}{3}\pi (5)^3 = 523.6) cm³.

A cylinder has a radius of (3) centimeters and a height of (8) centimeters. What is the volume of the cylinder?

  1. (75.4) cm³

  2. (94.2) cm³

  3. (113.1) cm³

  4. (131.9) cm³


Correct Option: A
Explanation:

The volume of a cylinder is given by (\pi r^2 h). Substituting (r = 3) cm and (h = 8) cm, we get (\pi (3)^2 (8) = 75.4) cm³.

A cone has a radius of (4) centimeters and a height of (10) centimeters. What is the volume of the cone?

  1. (33.5) cm³

  2. (54.9) cm³

  3. (76.4) cm³

  4. (97.8) cm³


Correct Option: A
Explanation:

The volume of a cone is given by (\frac{1}{3}\pi r^2 h). Substituting (r = 4) cm and (h = 10) cm, we get (\frac{1}{3}\pi (4)^2 (10) = 33.5) cm³.

A cube has a surface area of (150) square centimeters. What is the length of one side of the cube?

  1. (5) cm

  2. (6) cm

  3. (7) cm

  4. (8) cm


Correct Option: A
Explanation:

The surface area of a cube is given by (6s^2), where (s) is the length of one side. Solving for (s), we get (s = \sqrt{\frac{A}{6}}). Substituting (A = 150) cm², we get (s = \sqrt{\frac{150}{6}} = 5) cm.

A sphere has a surface area of (144) square centimeters. What is the radius of the sphere?

  1. (3) cm

  2. (4) cm

  3. (5) cm

  4. (6) cm


Correct Option: B
Explanation:

The surface area of a sphere is given by (4\pi r^2). Solving for (r), we get (r = \sqrt{\frac{A}{4\pi}}). Substituting (A = 144) cm², we get (r = \sqrt{\frac{144}{4\pi}} = 4) cm.

A cylinder has a surface area of (300) square centimeters. The radius of the base is (5) centimeters. What is the height of the cylinder?

  1. (10) cm

  2. (12) cm

  3. (14) cm

  4. (16) cm


Correct Option: A
Explanation:

The surface area of a cylinder is given by (2\pi r h + 2\pi r^2). Solving for (h), we get (h = \frac{A - 2\pi r^2}{2\pi r}). Substituting (A = 300) cm², (r = 5) cm, and (\pi \approx 3.14), we get (h = \frac{300 - 2\pi (5)^2}{2\pi (5)} = 10) cm.

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