Intermediate Geometry : Spheres

Study concepts, example questions & explanations for Intermediate Geometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #51 : Spheres

Find the surface area of a hemisphere that has a radius of .

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

, where  is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

Plug in the given radius to find the surface area.

Make sure to round to  places after the decimal.

Example Question #52 : Spheres

Find the surface area of a hemisphere if it has a radius of .

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

, where  is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

Plug in the given radius to find the surface area.

Make sure to round to  places after the decimal.

Example Question #53 : Spheres

Find the surface area of a hemisphere with a radius of .

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

, where  is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

Plug in the given radius to find the surface area.

Make sure to round to  places after the decimal.

Example Question #54 : Spheres

Find the surface area of a hemisphere with a radius of .

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

, where  is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

Plug in the given radius to find the surface area.

Make sure to round to  places after the decimal.

Example Question #55 : Spheres

Find the surface area of a hemisphere with a radius of .

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

, where  is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

Plug in the given radius to find the surface area.

Make sure to round to  places after the decimal.

Example Question #56 : Spheres

Find the surface area of a hemisphere that has a radius of .

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

, where  is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

Plug in the given radius to find the surface area.

Make sure to round to  places after the decimal.

Example Question #57 : Spheres

Find the surface area of a hemisphere that has a radius of .

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

, where  is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

Plug in the given radius to find the surface area.

Make sure to round to  places after the decimal.

Example Question #58 : Spheres

True or false: A sphere with radius 1 has surface area .

Possible Answers:

True

False

Correct answer:

False

Explanation:

Given radius , the surface area of a sphere  can be calculated according to the formula

Set :

The statement is false.

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

The surface area of a sphere is .  What is the diameter of the sphere?

Possible Answers:

Correct answer:

Explanation:

The surface area of a sphere is given by

So the equation to sovle becomes  or so

To answer the question we need to find the diameter:

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

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

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a sphere:

Plug in the volume and find the radius by solving for :

Start solving for  by multiplying both sides of the equation by :

Now, divide each side of the equation by :

Reduce the left side of the equation:

Finally, take the cubed root of both sides of the equation:

Keep in mind that you've solved for the radius, not the diameter. The diameter is double the radius, which is: .

Learning Tools by Varsity Tutors