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find the volume of a right circular cone that has a height of 10.7 in and a base with a diameter of 8.1 in. round your answer to the nearest tenth of a cubic inch.
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Explanation:

Step1: Find the radius of the base

The diameter of the base is \( 8.1 \) in, so the radius \( r \) is half of the diameter.
\( r=\frac{8.1}{2}=4.05 \) in.

Step2: Recall the volume formula for a cone

The volume \( V \) of a right circular cone is given by the formula \( V = \frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step3: Substitute the values into the formula

We know that \( r = 4.05 \) in and \( h = 10.7 \) in. Substituting these values into the formula:
\( V=\frac{1}{3}\times\pi\times(4.05)^{2}\times10.7 \)
First, calculate \( (4.05)^{2}=4.05\times4.05 = 16.4025 \)
Then, \( \frac{1}{3}\times16.4025\times10.7=\frac{16.4025\times10.7}{3} \)
\( 16.4025\times10.7 = 175.50675 \)
\( \frac{175.50675}{3}=58.50225 \)
Now, multiply by \( \pi \): \( V = 58.50225\times\pi\approx58.50225\times3.14159\approx183.7 \) (rounded to the nearest tenth)

Answer:

\( 183.7 \)