Question

for a science project, alana constructed a cone to use as a mountain. the cone has a diameter of 10 in and a height of 15 in. what is the volume of the cone?
( \bigcirc ) ( 50pi \text{ in}^3 )
( \bigcirc ) ( 75pi \text{ in}^3 )
( \bigcirc ) ( 125pi \text{ in}^3 )
( \bigcirc ) ( 150pi \text{ in}^3 )

Explanation:

Step1: Find radius from diameter

The radius $r$ is half the diameter. Given diameter = 10 in,
$r = \frac{10}{2} = 5$ in

Step2: Recall cone volume formula

The volume $V$ of a cone is $V = \frac{1}{3}\pi r^2 h$

Step3: Substitute values and calculate

Substitute $r=5$ in, $h=15$ in:
$V = \frac{1}{3}\pi (5)^2 (15)$
$V = \frac{1}{3}\pi (25)(15)$
$V = \frac{1}{3} \times 375\pi$
$V = 125\pi$ in³

Answer:

125π in³ (matches the third option: 125π in³)