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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

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Example Question #9 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Possible Answers:

219.29

200.01

198.62

207.35

Correct answer:

207.35

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(3)^2+2\pi(3)(8)=66\pi=207.35$

Make sure to round to places after the decimal point.

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Example Question #10 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Possible Answers:

266.71

309.59

334.11

301.59

Correct answer:

301.59

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(4)^2+2\pi(4)(8)=96\pi=301.59$

Make sure to round to places after the decimal point.

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Example Question #11 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Possible Answers:

1187.52

1214.12

1167.89

1098.29

Correct answer:

1187.52

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(7)^2+2\pi(7)(20)=378\pi=1187.52$

Make sure to round to places after the decimal point.

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Example Question #12 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Possible Answers:

2142.57

2345.12

2209.29

2671.03

Correct answer:

2142.57

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(11)^2+2\pi(11)(20)=682\pi=2142.57$

Make sure to round to places after the decimal point.

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Example Question #11 : Cylinders

Find the surface area of the given cylinder.

Possible Answers:

2095.19

1992.40

2411.20

2349.91

Correct answer:

2349.91

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(11)^2+2\pi(11)(23)=748\pi=2349.91$

Make sure to round to places after the decimal point.

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Example Question #14 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Possible Answers:

2590.02

2488.14

2676.61

1052.19

Correct answer:

2488.14

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(11)^2+2\pi(11)(25)=792\pi=2488.14$

Make sure to round to places after the decimal point.

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Example Question #15 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Possible Answers:

104.29

213.63

197.27

299.58

Correct answer:

213.63

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(2)^2+2\pi(2)(15)=68\pi=213.63$

Make sure to round to places after the decimal point.

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Example Question #16 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Possible Answers:

358.14

346.70

399.51

290.05

Correct answer:

358.14

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(3)^2+2\pi(3)(16)=114\pi=358.14$

Make sure to round to places after the decimal point.

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Example Question #1051 : Intermediate Geometry

Find the surface area of the given cylinder.

Possible Answers:

923.63

471.20

488.66

471.20

Correct answer:

923.63

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(7)^2+2\pi(7)(14)=294\pi=923.63$

Make sure to round to places after the decimal point.

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Example Question #1052 : Intermediate Geometry

Inscribed

The above diagram shows a sphere inscribed inside a cylinder.

The sphere has a surface area of 100. Give the surface area of the cylinder.

Possible Answers:

$66\frac{2}{3}$

100

$133\frac{1}{3}$

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 surface area of the cylinder is

$A_{1} = 2\pi r (r+h)$

which, after substituting, is

$A_{1} = 2\pi r (r+2r)$

$A_{1} =2 \pi r (3r)$

$A_{1} =2\cdot 3 \cdot \pi r \cdot r$

$A_{1} = 6 \pi r^{2}$

The surface area of the sphere is

$A_{2} = 4 \pi r^{2}$

Therefore, the ratio of the former to the latter is

$\frac{A_{1} }{A_{2}}= \frac{6 \pi r^{2}}{4\pi r^{2}} = \frac{6}{4} = \frac{3}{2}$

and

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

That is, the cylinder has surface area $\frac{3}{2}$ that of the sphere. Therefore, this area is

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

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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #9 : How To Find The Surface Area Of A Cylinder

Example Question #10 : How To Find The Surface Area Of A Cylinder

Example Question #11 : How To Find The Surface Area Of A Cylinder

Example Question #12 : How To Find The Surface Area Of A Cylinder

Example Question #11 : Cylinders

Example Question #14 : How To Find The Surface Area Of A Cylinder

Example Question #15 : How To Find The Surface Area Of A Cylinder

Example Question #16 : How To Find The Surface Area Of A Cylinder

Example Question #1051 : Intermediate Geometry

Example Question #1052 : Intermediate Geometry

All Intermediate Geometry Resources

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