Intermediate Geometry : Spheres

Study concepts, example questions & explanations for Intermediate Geometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #71 : Spheres

Find the diameter of a sphere if it has a volume of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

Make sure to round to  places after the decimal.

Example Question #72 : Spheres

Find the diameter of a sphere that has a volume of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

Make sure to round to  places after the decimal.

Example Question #11 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

Make sure to round to  places after the decimal.

Example Question #74 : Spheres

Find the diameter of a sphere if it has a volume of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

Make sure to round to  places after the decimal.

Example Question #75 : Spheres

Find the diameter of a sphere if its volume is .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

Make sure to round to  places after the decimal.

Example Question #76 : Spheres

Find the diameter of a sphere if it has a volume of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

Make sure to round to  places after the decimal.

Example Question #77 : Spheres

A company wants to construct an advertising balloon spherical in shape. It can afford to buy 28,000 square meters of material to make the balloon. What is the largest possible diameter of this balloon (nearest whole meter)?

Possible Answers:

Correct answer:

Explanation:

This is equivalent to asking the diameter of a balloon with surface area 28,000 square meters.

The relationship between the surface area  and the radius  is:

To find the radius, substitute for the surface area, then solve:

To find the diameter , double the radius—this is 94.

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. 

 

Learning Tools by Varsity Tutors