Question

Volume of Cones Practice
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Question
A water tank in the shape of a cone has a diameter of 12 feet and a height of 15 feet. What volume of water, in cubic feet, can the tank hold? Round your answer to the nearest tenth and use 3.14 for π
.

Answer 1

To find the volume of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

Where:
- \( V \) is the volume
- \( r \) is the radius of the base
- \( h \) is the height of the cone
- \( \pi \) is a constant approximately equal to 3.14

Given:
- The diameter of the cone is 12 feet, so the radius \( r \) is:
\[
r = \frac{12}{2} = 6 \text{ feet}
\]
- The height \( h \) is 15 feet.

Now plug in the values into the formula:

\[
V = \frac{1}{3} \times 3.14 \times (6)^2 \times 15
\]
\[
V = \frac{1}{3} \times 3.14 \times 36 \times 15
\]
\[
V = \frac{1}{3} \times 3.14 \times 540
\]
\[
V = \frac{1}{3} \times 1698
\]
\[
V = 566 \text{ (approximately)}
\]

Now, rounding to the nearest tenth as requested, the volume of water the tank can hold is approximately:

\[
\boxed{566.0} \text{ cubic feet}
\]