Intermediate Geometry : Cubes

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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

A rectangular prism with a square base is cut out of a cube as shown by the figure below.

8

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

Start by finding the volume of the cube.

Next, find the volume of the rectangular prism.

Subtract the volume of the rectangular prism from that of the cube to find the volume of the figure.

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

A rectangular prism with a square base is cut out of a cube as shown by the figure below.

9

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

Start by finding the volume of the cube.

Next, find the volume of the rectangular prism.

Subtract the volume of the rectangular prism from that of the cube to find the volume of the figure.

Example Question #63 : Cubes

A rectangular prism with a square base is cut out of a cube as shown by the figure below.

1

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

Start by finding the volume of the cube.

Next, find the volume of the rectangular prism.

Subtract the volume of the rectangular prism from that of the cube to find the volume of the figure.

Example Question #1021 : Intermediate Geometry

A rectangular prism with a square base is cut out of a cube as shown by the figure below.

11

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

Start by finding the volume of the cube.

Next, find the volume of the rectangular prism.

Subtract the volume of the rectangular prism from that of the cube to find the volume of the figure.

Example Question #1022 : Intermediate Geometry

A rectangular prism with a square base is cut out of the cube as shown by the figure below.

10

Find the volume of the figure.

Possible Answers:

Correct answer:

Explanation:

13

Start by finding the volume of the cube.

Next, find the volume of the rectangular prism.

Subtract the volume of the rectangular prism from that of the cube to find the volume of the figure.

Example Question #66 : Cubes

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

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.

Example Question #31 : How To Find The Volume Of A Cube

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.

Example Question #61 : Cubes

A sphere with a radius of  is cut out of a cube with 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.

Example Question #62 : Cubes

A sphere with a radius of  is cut out of a cube with 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.

Example Question #63 : Cubes

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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