Question

how do you find the volume to the nearest cubic in of a cone whose radius is 12 in and hieght is 15 inches

Answer 1

You have to know the formula for the volume of a cone.
In high school, there's no other way.

Volume of a cone = (1 / 3) π (radius)² (height)

Volume = (1 / 3) π (12 inches)² (15 inches)

Volume = 720 π = 2,261.95 cubic inches

Rounded to the nearest cubic inch, that's 2,262 cubic inches.

Answer 2

$V \beta = \frac{1}{3} \pi r^{2}h \\ V \beta = \frac{1}{3} \pi 12^{2} * 15 \\ V \beta = 2160 * \frac{1}{3} \pi \\ V \beta = 720 \pi$