GRE Math : How to find the radius of a sphere

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #342 :Geometry

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

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a sphere is

whereis the radius of the sphere.

Therefore,

, giving us.

Example Question #2 :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 #3 :How To Find The Radius Of A Sphere

What is the radius of a sphere with volumecubed 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.

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