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Intermediate Geometry : Spheres

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Example Questions

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

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

446.13

452.39

458.87

421.20

Correct answer:

452.39

Explanation:

Recall how to find the volume of a sphere:

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

Now since we only have half a sphere, divide the volume by .

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

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(6)^3=144\pi=452.39$

Make sure to round to places after the decimal.

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

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

691.32

718.38

710.02

729.06

Correct answer:

718.38

Explanation:

Recall how to find the volume of a sphere:

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

Now since we only have half a sphere, divide the volume by .

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

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(7)^3=\frac{686}{3}\pi=718.38$

Make sure to round to places after the decimal.

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Example Question #11 : Spheres

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

1120.30

1056.08

1098.67

1072.33

Correct answer:

1072.33

Explanation:

Recall how to find the volume of a sphere:

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

Now since we only have half a sphere, divide the volume by .

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

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(8)^3=\frac{1024}{3}\pi=1072.33$

Make sure to round to places after the decimal.

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

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is $\frac{1}{3}$ , what is the volume of the figure?

Possible Answers:

0.09

0.08

0.06

0.07

Correct answer:

0.08

Explanation:

Recall how to find the volume of a sphere:

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

Now since we only have half a sphere, divide the volume by .

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

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(\frac{1}{3})^3=\frac{2}{81}\pi=0.08$

Make sure to round to places after the decimal.

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Example Question #12 : Spheres

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

1526.81

1613.25

1589.67

1540.20

Correct answer:

1526.81

Explanation:

Recall how to find the volume of a sphere:

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

Now since we only have half a sphere, divide the volume by .

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

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(9)^3=486\pi=1526.81$

Make sure to round to places after the decimal.

Report an Error

Example Question #16 : How To Find The Volume Of A Sphere

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

2032.70

2094.40

2100.03

2086.20

Correct answer:

2094.40

Explanation:

Recall how to find the volume of a sphere:

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

Now since we only have half a sphere, divide the volume by .

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

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(10)^3=\frac{2000}{3}\pi=2094.40$

Make sure to round to places after the decimal.

Report an Error

Example Question #17 : How To Find The Volume Of A Sphere

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

2787.64

2558.95

2633.32

2704.05

Correct answer:

2787.64

Explanation:

Recall how to find the volume of a sphere:

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

Now since we only have half a sphere, divide the volume by .

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

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(11)^3=\frac{2662}{3}\pi=2787.64$

Make sure to round to places after the decimal.

Report an Error

Example Question #11 : Spheres

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

Find the volume of the figure.

Possible Answers:

1824.50

1811.21

1809.56

1804.26

Correct answer:

1809.56

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:

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

$\text{Volume of Cylinder}=\pi\times 6^2 \times 12=432 \pi$

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.

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 6^3=144\pi$

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

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

$\text{Volume of Figure}=432\pi + 144\pi=576\pi=1809.56$

Remember to round to places after the decimal.

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Example Question #13 : Spheres

A sphere is cut in half and is 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:

3219.59

3058.29

3027.45

3190.21

Correct answer:

3027.45

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:

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

$\text{Volume of Cylinder}=\pi\times 7^2 \times 15=735\pi$

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.

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 7^3=\frac{686}{3}\pi$

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

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

$\text{Volume of Figure}=735\pi + \frac{686}{3}\pi=3027.45$

Remember to round to places after the decimal.

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Example Question #14 : 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:

590.24

536.17

544.12

526.89

Correct answer:

536.17

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:

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

$\text{Volume of Cylinder}=\pi\times 4^2 \times 8=128\pi$

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.

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

$\text{Volume of Figure}=128\pi + \frac{128}{3}\pi=536.17$

Remember to round to places after the decimal.

Report an Error

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Intermediate Geometry : Spheres

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

Example Question #11 : Spheres

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

Example Question #12 : Spheres

Example Question #16 : How To Find The Volume Of A Sphere

Example Question #17 : How To Find The Volume Of A Sphere

Example Question #11 : Spheres

Example Question #13 : Spheres

Example Question #14 : Spheres

All Intermediate Geometry Resources

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