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High School Math : Cylinders

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Example Question #1 : Cylinders

This figure is a right cylinder with radius of 2 m and a height of 10 m.

What is the surface area of the right cylinder (m²)?

Possible Answers:

62.83

25.14

125.66

125.71

150.80

Correct answer:

150.80

Explanation:

In order to find the surface area of a right cylinder you must find the area of both bases (the circles on either end) and add them to the lateral surface area. The area of the two circles is easy to find with but remember to multiply by 2 for both bases

$2\cdot2^{2}\cdot\pi= 25.14$ .

Next find the lateral area. The lateral area if unrounded would be a rectangle with height of 10 m and length equal to the circumference of the base circles. Thus the lateral area is

$4\cdot\pi\cdot10= 125.66$

Now add the lateral area to the area of the two bases:

25.14 +125.66=150.80

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Example Question #2 : Cylinders

Find the surface area of a cylinder given that its radius is 2 and its height is 3.2.

Possible Answers:

20.8

$8\pi$

$20.8\pi$

$12.8\pi$

Correct answer:

$20.8\pi$

Explanation:

The standard equation to find the surface area of a cylinder is

$Surface\ Area=2\pi r^2+2\pi rh$

where denotes the radius and denotes the height.

Plug in the given values for and to find the area of the cylinder:

$Area=2\pi (2)^2+2\pi (2)(3.2)=8\pi +12.8\pi =20.8\pi$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

The base of a cylinder has an area of $9\pi$ and the cylinder has a height of . What is the surface area of this cylinder?

Possible Answers:

$90\pi$

$18\pi$

$72\pi$

Correct answer:

$90\pi$

Explanation:

The standard equation for the surface area of a cylinder is

$SA=2\pi r^2+2\pi rh$

where denotes radius and denotes height. We've been given the height in the question, so all we're missing is the radius. However, we are able to find the radius from the area of the circle:

$Area=\pi r^2$

We know the area is $9\pi$

$9\pi =\pi r^2$ so r=3

Now that we have both and , we can plug them into the standard equation for the surface area of a cylinder:

$SA=2\pi (3)^2+2\pi (3)(12)=18\pi +72\pi =90\pi$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

Find the surface area of the following cylinder.

Cylinder

Possible Answers:

$246 \pi m^2$

$252 \pi m^2$

$260 \pi m^2$

$240 \pi m^2$

$256 \pi m^2$

Correct answer:

$252 \pi m^2$

Explanation:

The formula for the surface area of a cylinder is:

$SA = lateral\ area + 2\cdot (base)$

$SA = 2 \pi r (h) + 2 (\pi r^2)$

where is the radius of the base and is the length of the height.

Plugging in our values, we get:

$SA = 2 \pi (7m) (11m) + 2 \pi (7m)^2$

$SA = 154 \pi m^2 + 98 \pi m^2 = 252 \pi m^2$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

Find the surface area of the following cylinder.

Cylinder

Possible Answers:

$114 \pi m^2$

$104 \pi m^2$

$124 \pi m^2$

$94 \pi m^2$

$84 \pi m^2$

Correct answer:

$104 \pi m^2$

Explanation:

The formula for the surface area of a cylinder is:

SA = 2(base)+(circumference)(height)

$SA = 2(\pi r^2)+(2 \pi r h)$

Where is the radius of the cylinder and is the height of the cylinder

Plugging in our values, we get:

$SA = 2\pi (4m)^2 + 2 \pi (4m)(9m)$

$SA = 104 \pi m^2$

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Example Question #2 : Cylinders

Find the surface area of the following partial cylinder.

Cylinder_sector

Possible Answers:

$\frac{104 \pi m^2}{3} + 80m^2$

$\frac{80 \pi m^2}{3} + 144m^2$

$144 \pi m^2+ 80m^2$

$\frac{144 \pi m^2}{6} + 80m^2$

$\frac{144 \pi m^2}{2} + 80m^2$

Correct answer:

$\frac{104 \pi m^2}{3} + 80m^2$

Explanation:

The formula for the surface area of this partial cylinder is:

SA = 2(base)(part)+2(face)+(circumference)(part)(height)

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

Where is the radius of the cylinder, is the height of the cylinder, and part is the sector of the cylinder.

Plugging in our values, we get:

$SA = 2(\pi (8m)^2)\left(\frac{60}{360}\right)+2(8m)(5m)+(2 \pi (8m))\left(\frac{60}{360}\right)(5m)$

$SA = \frac{64 \pi m^2}{3} + 80m^2 + \frac{40 \pi m^2}{3}$

$SA = \frac{104 \pi m^2}{3} + 80m^2$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

Find the surface area of the following partial cylinder.

Partial_cylinder

Possible Answers:

$200 \pi m^2 + 240m^2$

$234 \pi m^2 + 234m^2$

$240 \pi m^2 + 240m^2$

$234 \pi m^2 + 200m^2$

$234 \pi m^2 + 240m^2$

Correct answer:

$234 \pi m^2 + 240m^2$

Explanation:

The formula for the surface area of this partial cylinder is:

SA = 2(base)(part)+2(face)+(circumference)(part)(height)

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

where is the radius of the cylinder, is the height of the cylinder, and part is the sector of the cylinder.

Plugging in our values, we get:

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

$SA = 2(\pi (6m)^2)\left(\frac{270}{360}\right)+2(6m)(20m)+(2\pi (6m))\left(\frac{270}{360}\right)(20m)$

$SA = 54 \pi m^2 + 240m^2 +180 \pi m^2$

$SA = 234 \pi m^2 + 240m^2$

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Example Question #1 : Cylinders

What is the surface area of cylinder with a radius of 3 and height of 7?

Possible Answers:

$63\pi$

$51\pi$

$10\pi$

$21\pi$

Correct answer:

$51\pi$

Explanation:

The surface area of a cylinder can be determined by the following equation:

$SA=2\pi rh+\pi r^2$

$SA=(2\pi)(3)(7)+\pi(3^2)$

$SA=42\pi+9\pi=51\pi$

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Example Question #1 : Cylinders

What is the volume of a cylinder with a radius of 2 and a length that is three times as long as its diameter?

Possible Answers:

$48\pi$

$16\pi$

$12\pi$

Correct answer:

$48\pi$

Explanation:

The volume of a cylinder is the base multiplied by the height or length. The base is the area of a circle, which is $\pi r^{2}$ . Here, the radius is 2. The diameter is 4. Three times the diameter is 12. The height or length is 12. So, the answer is $48\pi$ .

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Example Question #1 : Cylinders

A water glass has the shape of a right cylinder. The glass has an interior radius of 2 inches, and a height of 6 inches. The glass is 75% full. What is the volume of the water in the glass (in cubic inches)?

Possible Answers:

$9 \pi$

$36 \pi$

$12 \pi$

$18 \pi$

$24 \pi$

Correct answer:

$18 \pi$

Explanation:

The volume of a right cylinder with radius r=2 and height h=6 is:

$\pi r^2 h = \pi (2)^2 (6) = 24 \pi$

Since the glass is only 75% full, only 75% of the interior volume of the glass is occupied by water. Therefore the volume of the water is:

$24 \pi \times ( 75 / 100 ) = 24 \pi (0.75) = 18 \pi$

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High School Math : Cylinders

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Cylinders

Example Question #2 : Cylinders

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #2 : Cylinders

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #1 : Cylinders

Example Question #1 : Cylinders

Example Question #1 : Cylinders

All High School Math Resources

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