High School Math : Geometry

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #691 : Geometry

What is the surface area of a sphere with a radius of ?

Possible Answers:

Correct answer:

Explanation:

To solve for the surface area of a sphere you must remember the formula:

First, plug the radius into the equation for :

Since , the surface area is .

The answer is therefore .

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

What is the diameter of a sphere with a volume of ?

Possible Answers:

Correct answer:

Explanation:

To find the diameter of a sphere we must use the equation for the volume of a sphere to find the radius which is half of the diameter.

The equation is

First we enter the volume into the equation yielding 

We then divide each side by  to get 

We then multiply each side by  to get 

We then take the cubic root of each side to solve for the radius 

The radius is 

We then multiply the radius by 2 to find the diameter 

The answer for the diameter is .

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

The volume of a sphere is . What is the diameter?

Possible Answers:

Correct answer:

Explanation:

To find the diameter of the sphere, we need to find the radius.

The volume of a sphere is .

Plug in our given values.

Notice that the 's cancel out.

The diameter is twice the radius, so .

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

If the surface area of a sphere is , find the diameter of this sphere. 

 

Possible Answers:

Correct answer:

Explanation:

The standard equation to find the surface area of a sphere is 

 where  denotes the radius. Rearrange this equation in terms of :

Substitute the given surface area into this equation and solve for the radius and then double the radius to get the diameter:

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

Given that the volume of a sphere is , find the diameter. 

Possible Answers:

Correct answer:

Explanation:

The standard equation to find the volume of a sphere is 

 where  denotes the radius. Rearrange this equation in terms of :

Substitute the given volume into this equation and solve for the radius. Double the radius to find the diameter:

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

What is the diameter of a sphere with a volume of ?

Possible Answers:

Correct answer:

Explanation:

The volume of a sphere is determined by the following equation:

Example Question #691 : Geometry

Find the radius of a sphere whose surface area is .

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

We know that the surface area of the spere is .

Rearrange and solve for .

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

What is the radius of a sphere that has a surface area of ?

Possible Answers:

Correct answer:

Explanation:

The standard equation to find the area of a sphere is  where  denotes the radius. Rearrange this equation in terms of :

To find the answer, substitute the given surface area into this equation and solve for the radius:

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

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

Possible Answers:

Correct answer:

Explanation:

The standard equation to find the volume of a sphere is 

where  denotes the radius. Rearrange this equation in terms of :

Substitute the given volume into this equation and solve for the radius:

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

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

Possible Answers:

Correct answer:

Explanation:

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