Question

a cone and a cylinder have the same base radius and height. if the cylinders volume is 300 cm³, what is the cones volume? a. 100 cm³ b. 200 cm³ c. 300 cm³ d. 150 cm³

Explanation:

Step1: Recall the volume formulas

The volume formula for a cylinder is \(V_{cylinder}=\pi r^{2}h\), and for 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 base radius \(r\) and height \(h\), if \(V_{cylinder}=\pi r^{2}h = 300\space cm^{3}\), then \(V_{cone}=\frac{1}{3}V_{cylinder}\).

Step3: Calculate the cone's volume

Substitute \(V_{cylinder} = 300\space cm^{3}\) into the formula for \(V_{cone}\). So \(V_{cone}=\frac{1}{3}\times300\).

$$V_{cone}= 100\space cm^{3}$$

Answer:

A. \(100\space cm^{3}\)