The volume of a right cone is 48π units^3. If its height is 9 units, find its circumference in terms of π

Answer 1

The formula for the volume of a cone is given by V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cone is 48π units^3 and the height is 9 units. Substituting these values into the formula, we get:

48π = (1/3)πr^2(9)

Simplifying the equation, we have:

48 = 3r^2

Dividing both sides by 3, we get:

16 = r^2

Taking the square root of both sides, we find:

r = 4

The radius of the cone is 4 units.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.

Substituting the value of r into the formula, we get:

C = 2π(4)

Simplifying, we find:

C = 8π

Therefore, the circumference of the right cone is 8π units.