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High School Math : High School Math

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Example Questions

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

What is the volume of a cylinder with a radius of and a height of ?

Possible Answers:

$9\pi+15$

$135\pi$

$96\pi$

$54\pi$

$9\pi$

Correct answer:

$135\pi$

Explanation:

When thinking of a 3D figure, think of it as a stack of something. In this case, a cylinder is a stack of a circles.

The volume will be the area of that base circle times the height of the cylinder. Mathematically that would be $V=(\pi r^2)*h$ .

Plug in our given values and solve.

$V=(\pi r^2)*h$

$V=(\pi (3)^2)*15$

$V=9\pi*15$

$V=135\pi$

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Example Question #117 : Solid Geometry

Find the volume of a cylinder given that its height and radius are 4 and 11, respectively.

Possible Answers:

$312\pi$

$484\pi$

$225\pi$

$144\pi$

$121\pi$

Correct answer:

$484\pi$

Explanation:

The standard equation to find the volume of a cylinder is

$V=\pi hr^2$

where denotes height and denotes radius.

Plug in the given values for height and radius to find the volume of the cylinder:

$V=\pi \cdot 4(11)^2=4\cdot 121\cdot\pi =484\pi$

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Example Question #118 : Solid Geometry

Find the volume of the following cylinder.

Cylinder

Possible Answers:

$545 \pi m^3$

$556 \pi m^3$

$539 \pi m^3$

$530 \pi m^3$

$521 \pi m^3$

Correct answer:

$539 \pi m^3$

Explanation:

The formula for the volume of a cylinder is:

$V = \pi r^2 h$

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

Plugging in our values, we get:

$V = \pi (7m)^2 (11m)$

$V = 539 \pi m^3$

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Example Question #119 : Solid Geometry

Find the volume of the following cylinder.

Cylinder

Possible Answers:

$134 \pi m^3$

$144 \pi m^3$

$124 \pi m^3$

$164 \pi m^3$

$154 \pi m^3$

Correct answer:

$144 \pi m^3$

Explanation:

The formula for the volume of a cylinder is:

V = (base)(height)

$V=(\pi r^2)(h)$

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

Plugging in our values, we get:

$V=\pi (4m)^2(9m)$

$V = 144 \pi m^3$

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

Find the volume of the following partial cylinder.

Cylinder_sector

Possible Answers:

$\frac{160 \pi m^3}{2}$

$\frac{160 \pi m^3}{4}$

$160 \pi m^3$

$\frac{160 \pi m^3}{6}$

$\frac{160 \pi m^3}{3}$

Correct answer:

$\frac{160 \pi m^3}{3}$

Explanation:

The formula for the volume of a partial cylinder is:

V = (base)(height)(part)

$V = (\pi r^2)(h)\left(\frac{part}{360}\right)$

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

Plugging in our values, we get:

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

$V = \frac{320 \pi m^3}{6}=\frac{160 \pi m^3}{3}$

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Example Question #21 : Cylinders

Find the volume of the following partial cylinder.

Partial_cylinder

Possible Answers:

$520 \pi m^3$

$530 \pi m^3$

$540 \pi m^3$

$550 \pi m^3$

$560 \pi m^3$

Correct answer:

$540 \pi m^3$

Explanation:

The formula for the volume of a partial cylinder is:

V = (base)(height)(part)

$V = (\pi r^2)(h)\left(\frac{part}{360}\right)$

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

Plugging in our values, we get:

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

$V=540 \pi m^3$

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

If a cylinder has a radius, $\small r$ , of 2 inches and a height, $\small h$ , of 5 inches, what is the total surface area of the cylinder?

Possible Answers:

$\small 70\pi$

$\small 18\pi$

$\small 28\pi$

$\small 24\pi$

$\small 36\pi$

Correct answer:

$\small 28\pi$

Explanation:

The total surface area will be equal to the area of the two bases added to the area of the outer surface of the cylinder. If "unwrapped" the area of the outer surface is simply a rectangle with the height of the cylinder and a base equal to the circumference of the cylinder base. We can use these relationships to find a formula for the total area of the cylinder.

$A=2A_{base}+A_{rectangle}$

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

Use the given radius and height to solve for the final area.

$\small 2\pi(2)^{2} + 2\pi (2)(5)$

$\small 8\pi + 20\pi$

$\small 28\pi$

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

The volume of a cylinder is $81\pi$ . If the radius of the cylinder is , what is the surface area of the cylinder?

Possible Answers:

$3\pi$

$72\pi$

$9\pi$

$81\pi$

$27\pi$

Correct answer:

$72\pi$

Explanation:

The volume of a cylinder is equal to:

$V=\pi r^2h$

Use this formula and the given radius to solve for the height.

$81\pi=\pi(3)^2h$

$81\pi=9\pi(h)$

h=9

Now that we know the height, we can solve for the surface area. The surface area of a cylinder is equal to the area of the two bases plus the area of the outer surface. The outer surface can be "unwrapped" to form a rectangle with a height equal to the cylinder height and a base equal to the circumference of the cylinder base. Add the areas of the two bases and this rectangle to find the total area.

$A=2A_{base}+A_{rec}$

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

Use the radius and height to solve.

$A=2\pi (3)^2+2\pi (3)(9)$

$A=18\pi+54\pi$

$A=72\pi$

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Example Question #2 : How To Find The Surface Area Of A Cylinder

What is the surface area of a cylinder with a base diameter of 6in and a height of 8in ?

Possible Answers:

$36\pi in^{2}$

$66\pi in^{2}$

$48\pi in^{2}$

$14\pi in^{2}$

None of the answers

Correct answer:

$66\pi in^{2}$

Explanation:

Area of a circle $A=\pi r^{2}=\pi(\frac{d}{2})^{2}=\pi(\frac{6}{2})^{2}=\pi(3)^{2}=9\pi in^{2}$

Circumference of a circle $C=\pi d=6\pi in^{2}$

Surface area of a cylinder $SA=2A+hC=2(9\pi)+8(6\pi)=18\pi+48\pi=66\pi in^{2}$

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Example Question #26 : Cylinders

A balloon, in the shape of a sphere, is filled completely with water. The surface area of the filled balloon is $144\pi$ . If all of the balloon's water was emptied into a cylindrical cup of base radius 4, how high would the water level be?

Possible Answers:

$4\pi$

Correct answer:

Explanation:

The surface area of a sphere is given by the formula

$S (sphere) = 4\pi*r^2$ , which here equals $144\pi$ . So

$4\pi*r^2 = 144\pi$

r^2 = 36

r = 6

To find out what the water level would be, we need to know how much water is in the balloon. So we need to find the volume of the balloon.

The amount of water that is in the balloon is

$V(sphere) = \frac{4\pi*r^3}{3}$

= $\frac{4\pi*6^3}{3}$

$288\pi$

The cylindrical column of water will have this volume, and will have base radius 4. Using the formula for volume of a cylinder, we can solve for the height of the column of water.

$V(cylinder) = \pi*r^2*h$ , where is the base radius 4 in this case.

$288\pi = \pi*(4^2)*h$

18 = h

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #117 : Solid Geometry

Example Question #118 : Solid Geometry

Example Question #119 : Solid Geometry

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

Example Question #21 : Cylinders

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

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

Example Question #2 : How To Find The Surface Area Of A Cylinder

Example Question #26 : Cylinders

All High School Math Resources

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