Question

1. the radius of the base of a cone is 4 cm and the height is 9 cm. what is the volume?

a. 36π
b. 48π
c. 24π
d. 12π

Explanation:

Step1: Recall the volume formula for a cone

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 4\space\text{cm}\) and \(h=9\space\text{cm}\), substitute into \(V=\frac{1}{3}\pi r^{2}h\). First, calculate \(r^{2}\): \(r^{2}=4^{2}=16\). Then, \(V=\frac{1}{3}\pi\times16\times9\).

Step3: Simplify the expression

\(V=\frac{1}{3}\times9\times16\pi\). Since \(\frac{1}{3}\times9 = 3\), then \(V=3\times16\pi=48\pi\space\text{cm}^{3}\).

Answer:

B. \(48\pi\)