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ume of a Cone Level 1
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Find the volume of a right circular cone that has a height of 2.7 ft and a base with a diameter of
14.4 ft. Round your answer to the nearest tenth of a cubic foot.
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Verified Answer :

GinnyAnswer

To find the volume of a right circular cone, we'll use the formula for the volume of a cone:

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

where \(\(\pi\)\) is a mathematical constant approximately equal to 3.14159, \(\(r\)\) is the radius of the cone's base, and \(\(h\)\) is the cone's height.

For our specific problem, we have:

- The diameter of the cone's base, \(\( d = 14.4 \)\) feet. Since the radius is half of the diameter, the radius \(\( r \)\) will be \(\( \frac{d}{2} = \frac{14.4}{2} = 7.2 \)\) feet.
- The height of the cone, \(\( h = 2.7 \)\) feet.

Now, let's substitute the radius and height into the formula for the volume of the cone:

\(\[ V = \frac{1}{3} \pi (7.2)^2 (2.7) \]\)

We square the radius:

\(\[ V = \frac{1}{3} \pi (51.84) (2.7) \]\)

Now, let's multiply \(\(51.84\)\) by \(\(2.7\)\):

\(\[ V = \frac{1}{3} \pi (139.968) \]\)

Next, we can calculate \(\( \frac{1}{3} \)\) of \(\(139.968\)\):

\(\[ V = \pi (46.656) \]\)

Lastly, it's time to multiply by \(\(\pi\)\):

\(\[ V = 146.6 \]\) cubic feet (with \(\(\pi\)\) approximated to its actual value in the final calculation).

So, the volume of the cone is \(\(146.6\)\) cubic feet rounded to the nearest tenth of a cubic foot.

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