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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

497.35

412.27

452.09

488.33

Correct answer:

497.35

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

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

$\text{Volume of Cube}=10^3=1000$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{8}{2}=4$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 4^2 \times 10=160\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=1000-160\pi=497.35$

Make sure to round to places after the decimal.

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Example Question #14 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

2708.58

2591.08

2596.31

2621.02

Correct answer:

2621.02

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

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

$\text{Volume of Cube}=15^3=3375$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{8}{2}=4$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 4^2 \times 15=240\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=3375-240\pi=2621.02$

Make sure to round to places after the decimal.

Report an Error

Example Question #11 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

3219.82

2998.74

3120.07

3291.75

Correct answer:

3291.75

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

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

$\text{Volume of Cube}=16^3=4096$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{8}{2}=4$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 4^2 \times 16=256\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=4096-256\pi=3291.75$

Make sure to round to places after the decimal.

Report an Error

Example Question #12 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

12.12

16.32

17.58

18.09

Correct answer:

17.58

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

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

$\text{Volume of Cube}=3^3=27$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{2}{2}=1$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 1^2 \times 3=3\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=27-3\pi=17.58$

Make sure to round to places after the decimal.

Report an Error

Example Question #13 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

256.39

180.58

255.04

210.20

Correct answer:

255.04

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

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

$\text{Volume of Cube}=7^3=343$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{4}{2}=2$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 2^2 \times 7=28\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=343-28\pi=255.04$

Make sure to round to places after the decimal.

Report an Error

Example Question #14 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

60.86

62.33

75.31

52.39

Correct answer:

60.86

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

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

$\text{Volume of Cube}=4^3=64$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{1}{2}=0.5$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 0.5^2 \times 4=\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=64-\pi=60.86$

Make sure to round to places after the decimal.

Report an Error

Example Question #55 : Cubes

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

Find the volume of the figure.

Possible Answers:

2055

2145

2235

1990

Correct answer:

2145

Explanation:

Start by finding the volume of the cube.

$\text{Volume of Cube}=\text{edge}^3$

$\text{Volume of Cube}=13^3=2197$

Next, find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=\text{width}\times\text{length}\times\text{height}$

$\text{Volume of Rectangular Prism}=2 \times 2 \times 13=52$

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

$\text{Volume of Figure}=\text{Volume of Cube}-\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=2197- 52=2145$

Report an Error

Example Question #56 : Cubes

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

Find the volume of the figure.

Possible Answers:

168

180

144

124

Correct answer:

168

Explanation:

Start by finding the volume of the cube.

$\text{Volume of Cube}=\text{edge}^3$

$\text{Volume of Cube}=7^3=343$

Next, find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=\text{width}\times\text{length}\times\text{height}$

$\text{Volume of Rectangular Prism}=5 \times5 \times 7=175$

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

$\text{Volume of Figure}=\text{Volume of Cube}-\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=343- 175=168$

Report an Error

Example Question #52 : Solid Geometry

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

Find the volume of the fgiure.

Possible Answers:

360

320

440

400

Correct answer:

360

Explanation:

Start by finding the volume of the cube.

$\text{Volume of Cube}=\text{edge}^3$

$\text{Volume of Cube}=10^3=1000$

Next, find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=\text{width}\times\text{length}\times\text{height}$

$\text{Volume of Rectangular Prism}=8 \times 8 \times 10=640$

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

$\text{Volume of Figure}=\text{Volume of Cube}-\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=1000- 640=360$

Report an Error

Example Question #53 : Solid Geometry

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

Possible Answers:

366

384

296

402

Correct answer:

384

Explanation:

Start by finding the volume of the cube.

$\text{Volume of Cube}=\text{edge}^3$

$\text{Volume of Cube}=8^3=512$

Next, find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=\text{width}\times\text{length}\times\text{height}$

$\text{Volume of Rectangular Prism}=4 \times4 \times 8=128$

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

$\text{Volume of Figure}=\text{Volume of Cube}-\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=512- 128=384$

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #11 : How To Find The Volume Of A Cube

Example Question #14 : How To Find The Volume Of A Cube

Example Question #11 : How To Find The Volume Of A Cube

Example Question #12 : How To Find The Volume Of A Cube

Example Question #13 : How To Find The Volume Of A Cube

Example Question #14 : How To Find The Volume Of A Cube

Example Question #55 : Cubes

Example Question #56 : Cubes

Example Question #52 : Solid Geometry

Example Question #53 : Solid Geometry

All Intermediate Geometry Resources

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