Section 8.2: 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. Find the volume of a cone with a height of $15.2$ meters and a radius of $4$ meters. Round to the nearest hundredth. The volume is approximately ___ cubic meters.

7. 7. A cone-shaped popcorn cup is $8$ inches tall and $6$ inches across at the base. Find its volume, rounding to the nearest hundredth. The volume is approximately ___ cubic inches.

8. 8. A cone-shaped teepee tent is $10$ feet tall and $10$ feet across at the base. Find its volume, rounding to the nearest hundredth. The volume is approximately ___ cubic feet.

9. 9. Find the volume of a cone with a height of $9$ feet and a radius of $2$ feet. Round to the nearest hundredth. The volume is approximately ___ cubic feet.

10. 10. Find the volume of a cone with a height of $8$ inches and a radius of $6$ inches. Round to the nearest hundredth. The volume is approximately ___ cubic inches.