Volumes of Spheres Practice — Grade 7 math

Lesson 3: Volumes of Spheres — Practice Questions

1. A hemisphere has a radius of 9 meters. What is its volume in terms of $\pi$? Your answer should be in the form of $N\pi$. The volume is ___ cubic meters.
2. What is the volume of a hemisphere with a diameter of 12 centimeters? Express your answer in terms of $\pi$.
- A. $72\pi \text{ cm}^3$
- B. $144\pi \text{ cm}^3$
- C. $288\pi \text{ cm}^3$
- D. $1152\pi \text{ cm}^3$
3. Calculate the volume of a hemisphere with a radius of 2 inches. Express your answer as a fraction in terms of $\pi$ (e.g. $\frac{a\pi}{b}$). The volume is ___ cubic inches.
4. A complete sphere has a volume of $96\pi$ cubic units. What is the volume of a hemisphere with the same radius?
- A. $24\pi \text{ cubic units}$
- B. $48\pi \text{ cubic units}$
- C. $96\pi \text{ cubic units}$
- D. $192\pi \text{ cubic units}$
5. An architectural dome is a hemisphere with a diameter of 2 yards. What is the volume of the dome? Express your answer as a fraction in terms of $\pi$. The volume is ___ cubic yards.
6. A sphere has a volume of $36\pi$ cubic centimeters. What is its radius in centimeters? The radius is ___.
7. Which formula correctly shows how to find the radius $r$ of a sphere given its volume $V$?
- A. $r = \sqrt[3]{\frac{4V}{3\pi}}$
- B. $r = \sqrt[3]{\frac{3V}{4\pi}}$
- C. $r = \frac{3}{4}\pi V^3$
- D. $r = \frac{4}{3}\pi \sqrt[3]{V}$
8. A spherical water tank has a volume of approximately $523.6$ cubic feet. Using $\pi \approx 3.14$, what is the approximate radius of the tank in feet? The radius is ___ feet.
9. A dome is in the shape of a hemisphere and has a volume of $486\pi$ cubic meters. What is the radius of the dome's base in meters? The radius is ___ meters.
10. A sphere has a volume of $V$. If the volume of the sphere is multiplied by 8, what is the effect on its radius?
- A. The radius is multiplied by 2.
- B. The radius is multiplied by 4.
- C. The radius is multiplied by 8.
- D. The radius is multiplied by 64.