Question

paula measured a cone with a radius of 4 centimeters and a height of 12 centimeters. what is the volume of the cone?
round your answer to the nearest whole number.
\boxed{} cubic centimeters
then, paula measured a sphere with the same radius as the cone, 4 centimeters. what is the ratio of the cones volume to the spheres volume?
\frac{1}{3} \quad \frac{1}{4} \quad \frac{3}{4} \quad \frac{4}{3}

Explanation:

Step1: Calculate the volume of the cone

The formula for the volume of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). Given \(r = 4\) cm and \(h=12\) cm.
Substitute the values into the formula:
\(V_{cone}=\frac{1}{3}\times\pi\times4^{2}\times12\)
\(=\frac{1}{3}\times\pi\times16\times12\)
\(=64\pi\approx 64\times 3.14 = 200.96\approx201\) (cubic centimeters)

Step2: Calculate the volume of the sphere

The formula for the volume of a sphere is \(V_{sphere}=\frac{4}{3}\pi r^{3}\). Given \(r = 4\) cm.
Substitute the value into the formula:
\(V_{sphere}=\frac{4}{3}\pi\times4^{3}=\frac{4}{3}\pi\times64=\frac{256}{3}\pi\)

Step3: Calculate the ratio of the cone's volume to the sphere's volume

\(\text{Ratio}=\frac{V_{cone}}{V_{sphere}}=\frac{64\pi}{\frac{256}{3}\pi}\)
Cancel out \(\pi\) (since \(\pi
eq0\)):
\(\text{Ratio}=\frac{64}{\frac{256}{3}}=64\times\frac{3}{256}=\frac{3}{4}\)

Answer:

The volume of the cone is \(201\) cubic centimeters. The ratio of the cone's volume to the sphere's volume is \(\frac{3}{4}\) (the third option).