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, and \( \pi \) is approximately 3.14.

1. First, find the radius \( r \):

   • The diameter of the cone is 12 feet, so the radius is: \[ r = \frac{d}{2} = \frac{12}{2} = 6 \text{ feet} \]

2. Now use the height \( h = 15 \) feet.

3. Substitute the values into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times (6)^2 \times 15 \]

4. Calculate \( (6)^2 \): \[ (6)^2 = 36 \]

5. Substitute this into the equation: \[ V = \frac{1}{3} \times 3.14 \times 36 \times 15 \]

6. Calculate \( 36 \times 15 \): \[ 36 \times 15 = 540 \]

7. Substitute this back into the equation: \[ V = \frac{1}{3} \times 3.14 \times 540 \]

8. Now calculate \( 3.14 \times 540 \): \[ 3.14 \times 540 = 1695.6 \]

9. Finally, divide by 3: \[ V = \frac{1695.6}{3} = 565.2 \]

Rounding \( 565.2 \) to the nearest tenth gives:

\[ \text{The volume of water the tank can hold is } \boxed{565.2} \text{ cubic feet.} \]