Question

study the figure. if the cylinders volume is 900π cubic units, what is the volume of the cone? express your answer in terms of π.

Explanation:

Step1: Recall the volume formulas

The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\), and the volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\).

Step2: Analyze the relationship

Since the cone and the cylinder have the same radius \(r\) and height \(h\), and \(V_{cylinder}=\pi r^{2}h = 900\pi\).
Then \(V_{cone}=\frac{1}{3}V_{cylinder}\) (because \(V_{cone}=\frac{1}{3}\pi r^{2}h\) and \(V_{cylinder}=\pi r^{2}h\)).

Step3: Calculate the volume of the cone

Substitute \(V_{cylinder}=900\pi\) into the formula \(V_{cone}=\frac{1}{3}V_{cylinder}\), we get \(V_{cone}=\frac{1}{3}\times900\pi\).
\(V_{cone}=300\pi\)

Answer:

\(300\pi\)