Intermediate Geometry : Spheres

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #21 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

4

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #22 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

5

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #23 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

6

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #24 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

7

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #25 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

8

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #26 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

9

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #27 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

10

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #28 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

11

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #29 : How To Find The Volume Of A Sphere

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

12

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

Next, find the volume of the half sphere.

Plug in the radius to find the volume of the half sphere.

Next, add up the two volumes together to find the volume of the figure.

Remember to round to  places after the decimal.

 

Example Question #30 : How To Find The Volume Of A Sphere

A sphere with a radius of  is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

Correct answer:

Explanation:

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

Plug in the given radius to find the volume.

Next, recall how to find the volume of a cube:

Plug in the given side length to find the volume of the cube.

Finally, subtract the volume of the sphere from the volume of the cube.

Make sure to round to  places after the decimal.

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