Question

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find the volume of a right circular cone that has a height of 11.1 cm and a base with a diameter of 17.2 cm. round your answer to the nearest tenth of a cubic centimeter.
answer attempt 1 out of 2
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Explanation:

Step1: Find the radius of the base

The diameter of the base is 17.2 cm, so the radius \( r=\frac{17.2}{2} = 8.6 \) cm.

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 of the base and \( h \) is the height. Here, \( h = 11.1 \) cm and \( r = 8.6 \) cm.

Step3: Substitute the values into the formula

\( V=\frac{1}{3}\times\pi\times(8.6)^{2}\times11.1 \)
First, calculate \( (8.6)^{2}=73.96 \)
Then, \( \frac{1}{3}\times\pi\times73.96\times11.1=\frac{1}{3}\times\pi\times820.956 \)
\( \frac{820.956}{3}\times\pi = 273.652\times\pi \)
Using \( \pi\approx3.14159 \), we get \( 273.652\times3.14159\approx859.7 \) (rounded to the nearest tenth)

Answer:

\( 859.7 \)