Question

1. 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. 150 cm³
b. 100 cm³
c. 200 cm³
d. 300 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 \(V_{cone}=\frac{1}{3}\pi r^{2}h\), where \(r\) is the base radius and \(h\) is the height.

Step2: Relate the volumes

Since the cone and cylinder have the same base radius and height (\(r\) and \(h\) are equal for both), 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 \(V_{cone}=\frac{1}{3}\times300 = 100\space cm^{3}\)

Answer:

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