The volume of the cylindrical candle is 6 cubic centimeters. What is the volume of the spherical candle? Explain.

To find the volume of the spherical candle, we need to first find the radius of the sphere.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder. In this case, V = 6 cubic centimeters.

Since the cylinder is also the circumscribed cylinder of the sphere, the height of the cylinder is equal to the diameter of the sphere. Therefore, the height of the cylinder is equal to 2r.

Substitute V = 6, h = 2r and the formula for the volume of a cylinder into the formula:

6 = πr^2(2r)
6 = 2πr^3
r^3 = 3/π
r = (3/π)^(1/3)

Now that we have the radius of the sphere, we can find the volume of the sphere using the formula for the volume of a sphere, V = (4/3)πr^3:

V = (4/3)π((3/π)^(1/3))^3
V = (4/3)π(3/π)
V = 4 cubic centimeters

Therefore, the volume of the spherical candle is 4 cubic centimeters.