Question

question
find the volume of a right circular cone that has a height of 6.7 in and a base with a diameter of 8.8 in. round your answer to the nearest tenth of a cubic inch.
answer attempt 1 out of 2
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Explanation:

Step1: Find the radius

The diameter is 8.8 in, so the radius \( r=\frac{8.8}{2}=4.4 \) in.

Step2: Recall the volume formula for a cone

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

Step3: Substitute the values

Substitute \( r = 4.4 \) in, \( h = 6.7 \) in into the formula:
\( V=\frac{1}{3}\times\pi\times(4.4)^{2}\times6.7 \)
First, calculate \( (4.4)^{2}=19.36 \)
Then, \( \frac{1}{3}\times\pi\times19.36\times6.7 \approx\frac{1}{3}\times3.1416\times19.36\times6.7 \)
Calculate \( 3.1416\times19.36\approx60.82 \)
Then \( 60.82\times6.7\approx407.5 \)
Then \( \frac{1}{3}\times407.5\approx135.8 \)

Answer:

\( 135.8 \)