Question

1. a cone has a height of 15 cm and a radius of 4 cm. what is its volume in terms of π?

a. 60π cm³
b. 80π cm³
c. 150π cm³
d. 120π cm³

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 and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 4\ \text{cm}\) and \(h=15\ \text{cm}\), substitute into \(V=\frac{1}{3}\pi r^{2}h\).
We get \(V=\frac{1}{3}\pi\times(4)^{2}\times15\).

Step3: Simplify the expression

First, calculate \((4)^{2}=16\). Then \(\frac{1}{3}\times16\times15\).
\(\frac{1}{3}\times15 = 5\), and \(5\times16=80\). So \(V = 80\pi\ \text{cm}^3\).

Answer:

B. \(80\pi\ \text{cm}^3\)