Question

1. a cone and a cylinder share the same height and radius. if the cones volume is 100 cm³, what is the cylinders volume?

a. 300 cm³
b. 200 cm³
c. 30 cm³
d. 33.33 cm³

Explanation:

Step1: Recall volume formulas

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

Step2: Relate cone and cylinder volumes

Since \(V_{cone}=\frac{1}{3}\pi r^{2}h = 100\space cm^{3}\), then \(V_{cylinder}=\pi r^{2}h\). Substituting \(\pi r^{2}h = 3\times V_{cone}\).

Step3: Calculate cylinder volume

\(V_{cylinder}=3\times100 = 300\space cm^{3}\)

Answer:

A. \(300\space cm^{3}\)