Intermediate Geometry : Spheres

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #4 : How To Find The Radius Of A Sphere

If the volume of a sphere is , what is the sphere's exact radius?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a sphere:

Plug in the given volume and solve for the radius, .

Start by multiplying each side of the equation by :

Now, divide each side of the equation by :

Finally, take the cubed root of each side of the equation:

Example Question #5 : How To Find The Radius Of A Sphere

Given the volume of a sphere is , what is the radius?

Possible Answers:

Correct answer:

Explanation:

The equation for the volume of a sphere is:

, where  is the length of the sphere's radius.

Plug in the given volume and solve for  to calculate the sphere's radius:

 

Example Question #6 : How To Find The Radius Of A Sphere

If the volume of a sphere is , what is the radius of the sphere?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a sphere is:

, where  is the sphere's radius.

Plug in the volume and solve for , the sphere's radius:

Example Question #7 : How To Find The Radius Of A Sphere

Find the radius of a sphere if the surface area is .

Possible Answers:

Correct answer:

Explanation:

The formula for the surface area of a sphere is:

Substitute the given value for the sphere's surface area into the equation and solve for  to find the radius:

Example Question #8 : How To Find The Radius Of A Sphere

Find the radius of a sphere if its surface area is .

Possible Answers:

Correct answer:

Explanation:

The surface area formula for a sphere is:

, where  is the sphere's radius.

Substitute the given value for the sphere's area into the equation and solve for  to find the radius:

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