Question

the radius of the cone is 3 in and y = 5 in. what is the volume of the cone in terms of π? 12π in³ 15π in³ 8π in³ 10π in³

Explanation:

Step1: Find the height of the cone

Use the Pythagorean theorem $x = \sqrt{y^{2}-r^{2}}$, where $r = 3$ and $y = 5$. So $x=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4$ in.

Step2: Calculate the volume of the cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 3$ and $h=x = 4$ into the formula. $V=\frac{1}{3}\pi\times3^{2}\times4=\frac{1}{3}\pi\times9\times4 = 12\pi$ in³.

Answer:

$12\pi$ in³