Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? StartFraction 50 Over 3 EndFraction feet cubed StartFraction 100 Over 3 EndFraction feet cubed 75 feet cubed 100 feet cubed

Answer 1

100/3

Explanation:

Answer 2

100/3 cubic feet.

Step-by-step:

In this case, if you observe the sphere, the height is simply two times the radius.

The formula to find the volume of a sphere is π * r^2 * h. The height is basically just 2r. And so, the edited formula becomes π * r^2 * 2r = 2 * π * r^3.

2 * π * r^3 = 50

π * r^3 = 25

r^3 = 7.957747155

r =
`\sqrt[3]{7.957747155}`

r = 1.996472712

Now that we have the measure of the radius, we can find the volume of the sphere!

(4 / 3) * π * r^3

(4/3) * π * (1.996472712)^3

= (4/3) * π * 7.957747155

= (4/3) * π * (25 / π)

= (4/3) * 25

= 100/3 cubic feet.

Hope this helps!