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

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.(1 point)
cubic feet

1 answer

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.

Given:

  • The diameter of the cone is 12 feet, so the radius \(r\) is half of that:

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

  • The height \(h\) is 15 feet.

Now, substituting the values into the volume formula:

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

Calculating \(6^2\):

\[ 6^2 = 36 \]

Now substituting that back into the volume equation:

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

Calculating \(36 \times 15\):

\[ 36 \times 15 = 540 \]

Now substituting that value into the volume formula:

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

Calculating \(3.14 \times 540\):

\[ 3.14 \times 540 = 1695.6 \]

Now taking one third of that:

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

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

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