SSAT Upper Level Math : How to find the volume of a sphere

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Possible Answers:

Correct answer:

Explanation:

The volume of a sphere, given its radius, is 

Set , solve for , and double that to get the diameter.

The diameter is twice this, or 12.4 yards.

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

The diameter of a sphere is . Give the volume of the sphere in terms of .

Possible Answers:

Correct answer:

Explanation:

The diameter of a sphere is  so the radius of the sphere would be 

 

The volume enclosed by a sphere is given by the formula:

 

 

 

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

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

Possible Answers:

Correct answer:

Explanation:

The volume enclosed by a sphere is given by the formula:

where  is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be meters. Now we can get:

 

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

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

Possible Answers:

Correct answer:

Explanation:

The volume of a sphere is:

 

Where is the radius of the sphere. We know the volume and can solve the formula for :

 

 inches

 

So we can get:

 

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

A sphere has a diameter of  inches. What is the volume of this sphere?

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

To find the volume of a sphere, use the following formula:

, where  is the radius of the sphere.

Now, because we are given the diameter of the sphere, divide that value in half to find the radius.

 

Now, plug this value into the volume equation.

  

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

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

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of the sphere.

The radius is half the diameter, which is five.  Substitute the value.

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

What is the volume of a sphere with diameter 12 feet?

Possible Answers:

None of the other answers are correct

Correct answer:

Explanation:

The radius of the sphere is half the diameter, or 6 feet; use the formula

 .

Setting :

 

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