A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 8 feet. Find the radius.

Question

I dont understand this.

Answer 1

Hi,

Here's how this one works:

The formula for the volume of a cylinder is V = π(r)^2(h), and the formula for the volume of a sphere is V = (4/3)π(r)^3. Since we know the cylinder has a height of 8, we can substitute this value in for h. Since the volumes of the two figures are equal to each other, we can set the two equations equal to each other. In other words:

π(r)^2(8) = (4/3)π(r)^3

From here we use algebra to solve for r.

Divide both sides by π to get (r)^2(8) = (4/3)(r)^3

Divide both sides by r^2 to get 8 = (4/3)r

Multiply both sides of the equation by (3/4) to get r = 6.

This answer can be verified with substitution, where both volumes will equal 288π.

Hope this helps!