Grade 8 math quiz: Calculate the volume of spheres

📚 Quick Study Guide

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• Definition: A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball.
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• Radius (r): The distance from the center of the sphere to any point on its surface.
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• Diameter (d): The distance across the sphere passing through its center; $d = 2r$.
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• Volume Formula: The volume (V) of a sphere is calculated using the formula: $V = \frac{4}{3}πr^3$, where $π$ (pi) is approximately 3.14159.
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• Key Steps to Calculate Volume:
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  1. Identify the radius (r) of the sphere.
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  2. Substitute the radius into the volume formula.
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  3. Calculate the volume using the value of π.

🧪 Practice Quiz

1. What is the formula for the volume of a sphere?
   1. $V = πr^2h$
   2. $V = \frac{1}{3}πr^2h$
   3. $V = \frac{4}{3}πr^3$
   4. $V = 2πr$
2. A sphere has a radius of 3 cm. What is its volume (use π ≈ 3.14)?
   1. 28.26 cm³
   2. 36 cm³
   3. 113.04 cm³
   4. 452.16 cm³
3. If the diameter of a sphere is 10 inches, what is its volume (use π ≈ 3.14)?
   1. 523.33 in³
   2. 4186.67 in³
   3. 418.67 in³
   4. 52.33 in³
4. A sphere has a volume of $36π$ cubic meters. What is its radius?
   1. 3 m
   2. 6 m
   3. 9 m
   4. 12 m
5. What happens to the volume of a sphere if you double its radius?
   1. The volume doubles.
   2. The volume quadruples.
   3. The volume increases by a factor of eight.
   4. The volume increases by a factor of sixteen.
6. A spherical balloon has a radius of 6 inches. How much air is needed to fully inflate the balloon (use π ≈ 3.14)?
   1. 904.32 in³
   2. 113.04 in³
   3. 226.08 in³
   4. 216 in³
7. A company wants to produce spherical ornaments with a volume of approximately 33.5 cubic centimeters. What radius should they use (use π ≈ 3.14)?
   1. 1 cm
   2. 2 cm
   3. 3 cm
   4. 4 cm