Question

the volume of a cylinder is 720π cubic units. what is the volume of a cone that shares the same base area and height as this cylinder? express your answer in terms of π. use the keypad to type your answer in the box provided. the volume of the cone is cubic units.

Explanation:

Step1: Recall the volume formulas

The volume formula of a cylinder is \(V_{cylinder}=B\times h\) (where \(B\) is the base - area and \(h\) is the height). The volume formula of a cone is \(V_{cone}=\frac{1}{3}B\times h\).

Step2: Use the relationship between the volumes

Since the cone and the cylinder have the same base area \(B\) and height \(h\), and \(V_{cylinder}=720\pi\) (i.e., \(B\times h = 720\pi\)).
Substitute \(B\times h\) into the cone's volume formula: \(V_{cone}=\frac{1}{3}(B\times h)\).

Step3: Calculate the volume of the cone

Substitute \(B\times h = 720\pi\) into \(V_{cone}=\frac{1}{3}(B\times h)\), we get \(V_{cone}=\frac{1}{3}\times720\pi\).

$$V_{cone}=240\pi$$

Answer:

\(240\pi\)