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
To find the volume of a cone-shaped water tank, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius of the cone's base, and \( h \) is the height of the cone. Since we are using \( \pi = 3.14 \), we can plug the values into the formula after we find the radius.
Given that the diameter of the cone is 12 feet, the radius (\( r \)) is half of that, which is:
\[ r = \frac{12 \text{ feet}}{2} = 6 \text{ feet} \]
Now, we plug the radius and height into the volume formula:
\[ V = \frac{1}{3} \cdot 3.14 \cdot (6 \text{ ft})^2 \cdot 15 \text{ ft} \]
\[ V = \frac{1}{3} \cdot 3.14 \cdot 36 \text{ ft}^2 \cdot 15 \text{ ft} \]
\[ V = \frac{1}{3} \cdot 3.14 \cdot 540 \text{ ft}^3 \]
\[ V = 3.14 \cdot 180 \text{ ft}^3 \]
\[ V = 565.2 \text{ ft}^3 \]
Therefore, the volume of the cone-shaped water tank is approximately \( 565.2 \) cubic feet. If you need to round it to the nearest tenth as indicated in the question, the volume is \( 565.2 \) cubic feet since it is already to the nearest tenth.