Intermediate Geometry : How to find the radius of a sphere

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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

 If the volume of a sphere is , what is the approximate length of its diameter?

 

Possible Answers:

Correct answer:

Explanation:

The correct answer is 6.12 ft.

 

Plug the value of  into the equation so that

  

Multiply both sides by 3 to get 

  

Then divide both sides by  to get

 

Then take the 3rd root of both sides to get 3.06 ft for the radius.  Finally, you have to multiply by 2 on both sides to get the diameter. Thus

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

The volume of a sphere is . What is its radius?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a sphere is: 

The only given information in the problem is the sphere's final volume. If the volume is , the formula for volume can be used to calculate the sphere's radius.

In this case, , the radius, is the only unknown variable that needs to be solved for. 

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

The area of a sphere is . What is its radius?

Possible Answers:

Correct answer:

Explanation:

The only information given is the area of

This problem may be approached "backwards," where the area formula for a sphere can be used to solve for the radius. This is possible because the formula for area is  , where  (the radius) is what we're looking for. After  is substituted in for the area, the goal is to solve for  by getting it by itself on one side of the equals sign. 

 

Example Question #314 : Solid Geometry

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 #315 : Solid Geometry

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 #81 : Spheres

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 #82 : Spheres

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 #83 : Spheres

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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