volume_mute
Volume of a Cone
publish date: 2026/05/18 20:42:21.100659 UTC
Find the volume of the cone shown below. (Use \(\pi \approx 3.14\) and round your final answer to the nearest hundredth).
Answer = (1)
Correct Answer
(1) 452.16
Explanation
The volume of a cone is exactly one-third of the volume of a cylinder with the same base and height: \(V = \frac{1}{3}\pi r^2 h\). Given \(r = 6\text{ in.}\) and \(h = 12\text{ in.}\):
\[ V = \frac{1}{3} \times 3.14 \times (6)^2 \times 12 \]
\[ V = \frac{1}{3} \times 3.14 \times 36 \times 12 = 3.14 \times 12 \times 12 = 452.16\text{ in.}^3 \]
Reference
Mathematics for college students