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

π
.(1 point)
cubic feet

1 answer

To calculate the volume of a cone, we use the formula:

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

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

Given that the diameter of the cone is 12 feet, we can find the radius:

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

The height \( h \) of the cone is given as 15 feet.

Now, we can substitute the values of \( r \), \( h \), and \( \pi \) (using 3.14) into the volume formula:

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

Calculating \( (6)^2 \):

\[ (6)^2 = 36 \]

Now substituting back into the volume formula:

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

Calculating \( 36 \times 15 \):

\[ 36 \times 15 = 540 \]

Now substitute that value back:

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

Calculating \( 3.14 \times 540 \):

\[ 3.14 \times 540 = 1695.6 \]

Now divide by 3:

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

Therefore, the volume of water that the tank can hold is:

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