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Intermediate Geometry : Cylinders

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Example Question #51 : Cylinders

Find the volume of the figure.

Possible Answers:

450000.12

562020.12

494800.84

485320.28

Correct answer:

494800.84

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

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

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 50^2 \times 75=187500\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 20^2 \times 75=30000\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=187500\pi-30000\pi=157500\pi=494800.84$

Make sure to round to places after the decimal.

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Example Question #52 : Cylinders

Find the volume of the figure.

Possible Answers:

16025.36

15833.63

14582.73

18552.20

Correct answer:

15833.63

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

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

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 16^2 \times 20=5120\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 2^2 \times 20=80\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=5120\pi-80\pi=5040\pi=15833.63$

Make sure to round to places after the decimal.

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Example Question #53 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

4490.97

4242.68

4412.15

4509.20

Correct answer:

4490.97

Explanation:

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

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{12}{2}=6$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (6)^2(20)}{2}=360\pi$

Next, recall how to find the volume of a rectangular prism.

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

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(12)(20)(14)=3360$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=360\pi+3360=4490.97$

Remember to round to places after the decimal.

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Example Question #54 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

86.60

88.21

85.55

87.74

Correct answer:

87.74

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{3}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{3}{2})^2(7)}{2}=\frac{63}{8}\pi$

Next, recall how to find the volume of a rectangular prism.

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

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(3)(7)(3)=63$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=\frac{63}{8}\pi+63=87.74$

Remember to round to places after the decimal.

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Example Question #55 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

2097.13

2014.56

2141.64

2088.69

Correct answer:

2097.13

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{9}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{9}{2})^2(15)}{2}=\frac{1215}{8}\pi$

Next, recall how to find the volume of a rectangular prism.

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

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(9)(15)(12)=1620$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=\frac{1215}{8}\pi+1620=2097.13$

Remember to round to places after the decimal.

Report an Error

Example Question #56 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Possible Answers:

2288.23

2678.92

2109.59

2389.55

Correct answer:

2288.23

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{12}{2}=6$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (6)^2(15)}{2}=270\pi$

Next, recall how to find the volume of a rectangular prism.

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

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(12)(15)(8)=1440$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=270\pi+1440=2288.23$

Remember to round to places after the decimal.

Report an Error

Example Question #57 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Possible Answers:

2241.20

2444.09

2590.15

2385.40

Correct answer:

2385.40

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{10}{2}=5$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (5)^2(20)}{2}=250\pi$

Next, recall how to find the volume of a rectangular prism.

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

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(10)(20)(8)=1600$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=250\pi+1600=2385.40$

Remember to round to places after the decimal.

Report an Error

Example Question #58 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Possible Answers:

4449.12

4443.22

4333.71

4902.56

Correct answer:

4443.22

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{13}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{13}{2})^2(17)}{2}=\frac{2873}{8}\pi$

Next, recall how to find the volume of a rectangular prism.

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

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(13)(17)(15)=3315$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=\frac{2873}{8}\pi+3315=4443.22$

Remember to round to places after the decimal.

Report an Error

Example Question #59 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

32.56

34.09

31.11

33.93

Correct answer:

33.93

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{1}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{1}{2})^2(10)}{2}=\frac{5}{4}\pi$

Next, recall how to find the volume of a rectangular prism.

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

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(1)(10)(3)=30$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=\frac{5}{4}\pi+30=33.93$

Remember to round to places after the decimal.

Report an Error

Example Question #60 : Cylinders

Inscribed

The above diagram shows a sphere inscribed inside a cylinder.

The sphere has a volume of 100. Give the volume of the cylinder.

Possible Answers:

125

$116\frac{1}{6}$

$133\frac{1}{3}$

120

150

Correct answer:

150

Explanation:

Let be the radius of the sphere. Then the radius of the base of the cylinder is also , and the height of the cylinder is h = 2r .

The volume of the cylinder is

$V_{1} = \pi r^{2} h$ ,

which, after substituting, is

$V _{1} = \pi r^{2} (2r)$

$V_{1} =2 \cdot \pi r^{2}\cdot r$

$V_{1} =2 \pi r^{3}$

The volume of the sphere is

$V_{2} = \frac{4}{3} \pi r^{3}$

Therefore, the ratio of the former to the latter is

$\frac{V_{1} }{V_{2}}=\frac{ 2 \pi r^{3}}{\frac{4}{3}\pi r^{3}}$

$\frac{V_{1} }{V_{2}}=\frac{ 2 }{\frac{4}{3} } = 2 \cdot \frac{3}{4} = \frac{3}{2}$

and

$V_{1} = \frac{3}{2}V_{2}$

That is, the volume of the cylinder is $\frac{3}{2}$ times that of the sphere, so the volume of the cylinder is

$V_{1} = \frac{3}{2} \cdot 100 = 150$ .

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Intermediate Geometry : Cylinders

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #51 : Cylinders

Example Question #52 : Cylinders

Example Question #53 : Cylinders

Example Question #54 : Cylinders

Example Question #55 : Cylinders

Example Question #56 : Cylinders

Example Question #57 : Cylinders

Example Question #58 : Cylinders

Example Question #59 : Cylinders

Example Question #60 : Cylinders

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