Lesson 2: Volumes of Cones — Practice Questions

1. 1. A cone has a volume of $128\pi$ cubic feet and its height is 6 feet. The radius of the cone's base is ___ feet.

2. 2. A cone-shaped cup has a volume of 200 cubic centimeters and a height of 6 centimeters. Which expression represents the radius of the cup?

   • A. $r = \sqrt{\frac{100}{\pi}}$
   • B. $r = \sqrt{\frac{200}{\pi}}$
   • C. $r = \frac{100}{\pi}$
   • D. $r = \sqrt{100\pi}$

3. 3. A cone has a volume of $50\pi$ cubic meters and a height of 3 meters. The radius of the cone is ___ meters.

4. 4. The volume of a cone is given by $V = \frac{1}{3}\pi r^2 h$. Which equation is correctly rearranged to solve for the radius, $r$?

   • A. $r = \sqrt{\frac{3V}{\pi h}}$
   • B. $r = \sqrt{\frac{V}{3\pi h}}$
   • C. $r = \frac{3V}{\pi h}$
   • D. $r = \sqrt{3V \pi h}$

5. 5. A cone has a volume of $\frac{16\pi}{3}$ cubic inches and a height of 4 inches. Its radius is ___ inches.

6. 6. A conical paper cup has a radius of 2 cm and a height of 9 cm. Its volume is ___ cubic cm. (Leave $\pi$ in your answer)

7. 7. A cone-shaped funnel has a volume of $32\pi$ cubic inches and a base radius of 4 inches. The height of the funnel is ___ inches.

8. 8. A decorative cone has a height of 7 inches and a circular base with a diameter of 6 inches. What is the volume of the cone in cubic inches?

   • A. $21\pi$
   • B. $84\pi$
   • C. $63\pi$
   • D. $14\pi$

9. 9. If the radius of a cone's base is doubled while its height remains the same, how does the new volume compare to the original volume?

   • A. It is 2 times larger.
   • B. It is 4 times larger.
   • C. It is 8 times larger.
   • D. It stays the same.