Question

the volume of a cone is \\( \frac { 1 } { 3 } \\) that of a cylinder when the radius and height are the same \\( \left( v = \frac { 1 } { 3 } \pi r ^ { 2 } h \
ight) \\). what is the volume of a cone with a radius of 14 inches and a height of 16 inches? (use pi and round to the nearest whole number) \\( v = \\) \\( \mathrm { in } ^ { 3 } \\)

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\).

Step2: Substitute the given values of \(r = 14\) inches and \(h=16\) inches into the formula

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Step3: Calculate the numerical value

Using \(\pi\approx3.14\), we have \(V=\frac{3136\times3.14}{3}=\frac{9846.04}{3}\approx3282.01\)

Step4: Round to the nearest whole number

Rounding \(3282.01\) to the nearest whole number gives \(3282\)

Answer:

\(3282\)