Question

find the volume of a right circular cone that has a height of 15 ft and a base with a radius of 7.9 ft. round your answer to the nearest tenth of a cubic foot.

answer attempt 1 out of 2

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Explanation:

Step1: Recall the formula for the volume of 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.

Step2: Substitute the given values into the formula

We are given that \( r = 7.9\) ft and \( h=15\) ft. Substituting these values into the formula, we get:
\( V=\frac{1}{3}\times\pi\times(7.9)^{2}\times15 \)
First, calculate \( (7.9)^{2}=7.9\times7.9 = 62.41 \)
Then, \( \frac{1}{3}\times15 = 5 \)
So the formula simplifies to \( V=\pi\times62.41\times5 \)

Step3: Calculate the numerical value

\( V = 312.05\pi \)
Using \( \pi\approx3.14159 \), we have \( V\approx312.05\times3.14159 \)
\( 312.05\times3.14159\approx312.05\times3 + 312.05\times0.14159\)
\( 312.05\times3 = 936.15\)
\( 312.05\times0.14159\approx312.05\times0.1 + 312.05\times0.04+312.05\times0.00159\)
\( 312.05\times0.1 = 31.205\)
\( 312.05\times0.04 = 12.482\)
\( 312.05\times0.00159\approx0.496\)
Adding these together: \( 31.205 + 12.482+0.496 = 44.183\)
Then \( 936.15+44.183 = 980.333\)
So \( V\approx980.3\) (rounded to the nearest tenth)

Answer:

\( 980.3 \)