Question

question
find the volume of a right circular cone that has a height of 6.5 cm and a base with a radius of 8.5 cm. round your answer to the
nearest tenth of a cubic centimeter.
answer
attempt 1 out of 2
cm³
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Explanation:

Step1: Recall the volume formula for a cone

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

Step2: Substitute the given values into the formula

Given \(r = 8.5\space cm\) and \(h=6.5\space cm\). Substitute these values into the formula:
\(V=\frac{1}{3}\times\pi\times(8.5)^{2}\times6.5\)
First, calculate \((8.5)^{2}=72.25\). Then the expression becomes \(V=\frac{1}{3}\times\pi\times72.25\times6.5\)
\(V=\frac{1}{3}\times\pi\times469.625\)
\(V=\frac{469.625\pi}{3}\)

Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(V=\frac{469.625\times3.14159}{3}\)
\(469.625\times3.14159 = 469.625\times(3 + 0.14159)=469.625\times3+469.625\times0.14159\)
\(469.625\times3 = 1408.875\), \(469.625\times0.14159\approx66.57\)
\(469.625\times3.14159\approx1408.875 + 66.57=1475.445\)
\(V=\frac{1475.445}{3}\approx491.8\)

Answer:

\(491.8\space cm^{3}\)