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Intermediate Geometry : Solid 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 #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.

Find the volume of the figure.

Possible Answers:

109.92

124.12

131.09

129.85

Correct answer:

129.85

Explanation:

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:

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

$\text{Volume of Cylinder}=\pi\times 2^2 \times 9=36\pi$

Next, find the volume of the half sphere.

$\text{Volume of Half sphere}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius}^3)=\frac{2}{3}\pi\times\text{radius}^3$

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

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 2^3=\frac{16}{3}\pi$

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

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=36\pi + \frac{16}{3}\pi=129.85$

Remember to round to places after the decimal.

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Example Question #21 : Spheres

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.

Find the volume of the figure.

Possible Answers:

254.47

249.88

258.10

249.31

Correct answer:

254.47

Explanation:

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:

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

$\text{Volume of Cylinder}=\pi\times 3^2 \times 7=63\pi$

Next, find the volume of the half sphere.

$\text{Volume of Half sphere}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius}^3)=\frac{2}{3}\pi\times\text{radius}^3$

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

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 3^3=18\pi$

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

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=63\pi + 18\pi=254.47$

Remember to round to places after the decimal.

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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.

Find the volume of the figure.

Possible Answers:

234.73

281.52

242.95

214.20

Correct answer:

242.95

Explanation:

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:

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

$\text{Volume of Cylinder}=\pi\times 2^2 \times 18=72\pi$

Next, find the volume of the half sphere.

$\text{Volume of Half sphere}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius}^3)=\frac{2}{3}\pi\times\text{radius}^3$

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

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 2^3=\frac{16}{3}\pi$

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

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=72\pi + \frac{16}{3}\pi=242.95$

Remember to round to places after the decimal.

Report an Error

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.

Find the volume of the figure.

Possible Answers:

12.49

15.79

13.44

17.80

Correct answer:

17.80

Explanation:

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:

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

$\text{Volume of Cylinder}=\pi\times 1^2 \times 5=5\pi$

Next, find the volume of the half sphere.

$\text{Volume of Half sphere}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius}^3)=\frac{2}{3}\pi\times\text{radius}^3$

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

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 1^3=\frac{2}{3}\pi$

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

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=5\pi + \frac{2}{3}\pi=17.80$

Remember to round to places after the decimal.

Report an Error

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.

Find the volume of the figure.

Possible Answers:

12.59

11.52

10.44

8.39

Correct answer:

11.52

Explanation:

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:

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

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

Next, find the volume of the half sphere.

$\text{Volume of Half sphere}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius}^3)=\frac{2}{3}\pi\times\text{radius}^3$

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

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 1^3=\frac{2}{3}\pi$

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

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=3\pi + \frac{2}{3}\pi=11.52$

Remember to round to places after the decimal.

Report an Error

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.

Find the volume of the figure.

Possible Answers:

938.29

945.58

922.45

990.05

Correct answer:

938.29

Explanation:

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:

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

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

Next, find the volume of the half sphere.

$\text{Volume of Half sphere}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius}^3)=\frac{2}{3}\pi\times\text{radius}^3$

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

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 4^3=\frac{128}{3}\pi$

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

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=256\pi + \frac{128}{3}\pi=938.29$

Remember to round to places after the decimal.

Report an Error

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.

Find the volume of the figure.

Possible Answers:

8224.57

8667.79

8377.58

8484.12

Correct answer:

8377.58

Explanation:

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:

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

$\text{Volume of Cylinder}=\pi\times 10^2 \times 20=2000\pi$

Next, find the volume of the half sphere.

$\text{Volume of Half sphere}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius}^3)=\frac{2}{3}\pi\times\text{radius}^3$

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

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 10^3=\frac{2000}{3}\pi$

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

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=2000\pi + \frac{2000}{3}\pi=8377.58$

Remember to round to places after the decimal.

Report an Error

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

A sphere with a radius of $\frac{3}{4}$ is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

5.51

7.61

6.09

6.23

Correct answer:

6.23

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.

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{3}{4})^3=\frac{9}{16}\pi$

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

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

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

$\text{Volume of Cube}=2^3=8$

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

$\text{Volume of Figure}=8-\frac{9}{16}\pi=6.23$

Make sure to round to places after the decimal.

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Example Question #1231 : Intermediate Geometry

A sphere with a radius of $\frac{7}{8}$ is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

24.12

22.01

24.19

20.04

Correct answer:

24.19

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.

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{7}{8})^3=\frac{343}{384}\pi$

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

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

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

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

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

$\text{Volume of Figure}=27-\frac{343}{384}\pi=24.19$

Make sure to round to places after the decimal.

Report an Error

Example Question #1232 : Intermediate Geometry

A sphere with a radius of $\frac{2}{5}$ is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

26.73

25.82

20.10

24.49

Correct answer:

26.73

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.

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{2}{5})^3=\frac{32}{375}\pi$

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

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

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

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

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

$\text{Volume of Figure}=27-\frac{32}{375}\pi=26.73$

Make sure to round to places after the decimal.

Report an Error

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All Intermediate Geometry Resources

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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

Example Question #21 : Spheres

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

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

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

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

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

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

Example Question #1231 : Intermediate Geometry

Example Question #1232 : Intermediate Geometry

All Intermediate Geometry Resources

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