Question

1. a cone has a radius of 3 m and a height of 6 m. a cylinder has the same dimensions. what is the ratio of the cones volume to the cylinders volume? a. 1:3 b. 1:1 c. 1:2 d. 2:3

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: Calculate the ratio

\(\frac{V_{cone}}{V_{cylinder}}=\frac{\frac{1}{3}\pi r^{2}h}{\pi r^{2}h}\). Cancel out \(\pi r^{2}h\) (since \(r = 3m\) and \(h=6m\) are same for both). We get \(\frac{1}{3}\).

Answer:

A. \(1:3\)