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
.(1 point)
cubic feet

Answer 1

To find the volume \( V \) of a cone, you can use the formula:

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

where \( r \) is the radius and \( h \) is the height.

1. **Find the radius**: The diameter of the cone is 12 feet, so the radius \( r \) is:

\[
r = \frac{d}{2} = \frac{12}{2} = 6 \text{ feet}
\]

2. **Use the height**: The height \( h \) is given as 15 feet.

3. **Plug the values into the formula**:

\[
V = \frac{1}{3} \times 3.14 \times (6)^2 \times 15
\]

4. **Calculate \( (6)^2 \)**:

\[
(6)^2 = 36
\]

5. **Substitute back into the formula**:

\[
V = \frac{1}{3} \times 3.14 \times 36 \times 15
\]

6. **Multiply**:

\[
36 \times 15 = 540
\]

7. **Now calculate**:

\[
V = \frac{1}{3} \times 3.14 \times 540
\]

8. **Multiply \( 3.14 \times 540 \)**:

\[
3.14 \times 540 = 1695.6
\]

9. **Divide by 3**:

\[
V = \frac{1695.6}{3} = 565.2
\]

So, the volume of water the tank can hold is approximately

\[
\boxed{565.2} \text{ cubic feet}.
\]