Question

consider the cylinder with a volume of 132π cm³. what is the volume of a cone with the same radius and height as the cylinder?

Explanation:

Step1: Recall the volume formulas

Volume of a cylinder \( V_{cylinder}=\pi r^{2}h\). Volume of a cone \( V_{cone}=\frac{1}{3}\pi r^{2}h\).

Step2: Relate the volumes

Given \( V_{cylinder} = 132\pi\) \(cm^{3}\) (i.e., \(\pi r^{2}h=132\pi\)). For the cone with the same \(r\) and \(h\), \(V_{cone}=\frac{1}{3}(\pi r^{2}h)\).

Step3: Substitute the value

Substitute \(\pi r^{2}h = 132\pi\) into the cone - volume formula. \(V_{cone}=\frac{1}{3}\times132\pi\).

$$V_{cone}= 44\pi$$

\(cm^{3}\)

Answer:

\(44\pi\ cm^{3}\)