Geometry Test Questions: Calculating Volume of Spheres

📚 Quick Study Guide

• 📏 Definition: A sphere is a perfectly round geometrical object in three-dimensional space, like a ball. All points on the surface are equidistant from the center.
• 🔢 Radius (r): The distance from the center of the sphere to any point on its surface.
• 📐 Diameter (d): The distance across the sphere passing through the center. It's twice the radius ($d = 2r$).
• ➗ Formula for Volume (V): The amount of space inside the sphere is calculated using the formula: $V = \frac{4}{3} \pi r^3$, where $\pi$ (pi) is approximately 3.14159.
• 💡 Key Tip: Make sure you are using the radius, not the diameter, in the volume formula. If given the diameter, divide it by 2 to get the radius.
• ➕ Units: Volume is always measured in cubic units (e.g., $cm^3$, $m^3$, $in^3$).

🧪 Practice Quiz

1. What is the volume of a sphere with a radius of 3 cm?
   1. A) 36π $cm^3$
   2. B) 9π $cm^3$
   3. C) 144π $cm^3$
   4. D) 4π $cm^3$
2. A sphere has a diameter of 10 inches. What is its volume?
   1. A) $\frac{500}{3}π$ $in^3$
   2. B) $\frac{250}{3}π$ $in^3$
   3. C) 100π $in^3$
   4. D) 1000π $in^3$
3. If the volume of a sphere is $\frac{32}{3}π$ $m^3$, what is its radius?
   1. A) 4 m
   2. B) 2 m
   3. C) 8 m
   4. D) 16 m
4. What is the volume of a sphere with a radius of 6 inches?
   1. A) 288π $in^3$
   2. B) 36π $in^3$
   3. C) 144π $in^3$
   4. D) 96π $in^3$
5. A spherical balloon has a diameter of 12 cm. What is its volume?
   1. A) 288π $cm^3$
   2. B) 36π $cm^3$
   3. C) 2304π $cm^3$
   4. D) 904.78 $cm^3$
6. If the radius of a sphere is doubled, how does the volume change?
   1. A) Volume is doubled
   2. B) Volume is quadrupled
   3. C) Volume is multiplied by 8
   4. D) Volume is multiplied by 16
7. A sphere has a volume of 36π $ft^3$. What is the length of its radius?
   1. A) 3 ft
   2. B) 6 ft
   3. C) 9 ft
   4. D) 12 ft