GRE Math : How to find the radius of a sphere

Example Questions

Example Question #41 : Solid Geometry

If a sphere has a volume of  cubic inches, what is the approximate radius of the sphere?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a sphere is

where  is the radius of the sphere.

Therefore,

, giving us .

Example Question #1 : How To Find The Radius Of A Sphere

A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?

Possible Answers:

Correct answer:

Explanation:

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

And thus the volume of the largest possible sphere to fit into this prism is

Example Question #2 : How To Find The Radius Of A Sphere

What is the radius of a sphere with volume  cubed units?

Possible Answers:

Correct answer:

Explanation:

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r:

Therefore, the radius of the sphere is 3.