Question

a cone has a height of 15 cm and a radius of 4 cm. what is its volume in terms of π?
a. 80π cm³
b. 120π cm³
c. 150π cm³
d. 60π 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 \(V=\frac{1}{3}\pi r^{2}h\):

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Step3: Simplify the expression

First, calculate \(\frac{1}{3}\times16\times15\). \(\frac{1}{3}\times15 = 5\), then \(5\times16=80\). So \(V = 80\pi\ \text{cm}^3\)

Answer:

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