find the radius of a cone with a volume of 477 mm^3 and a height of 28.5

The volume of a cone can be calculated using the formula:

V = (1/3)πr^2h

where V is the volume, r is the radius, and h is the height.

Plugging in the given values:

477 mm^3 = (1/3)πr^2 * 28.5

To isolate r, we can rearrange the equation:

r^2 = (3 * 477 mm^3) / (π * 28.5)

r^2 ≈ 50.32

Taking the square root of both sides, we get:

r ≈ √50.32

r ≈ 7.09 mm

Therefore, the radius of the cone is approximately 7.09 mm.