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High School Math : Cylinders

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

A circle has a circumference of $4\pi$ and it is used as the base of a cylinder. The cylinder has a surface area of $16\pi$ . Find the volume of the cylinder.

Possible Answers:

$8\pi$

$10\pi$

$4\pi$

$2\pi$

$6\pi$

Correct answer:

$8\pi$

Explanation:

Using the circumference, we can find the radius of the circle. The equation for the circumference is $2\pi r$ ; therefore, the radius is 2.

Now we can find the area of the circle using $\pi r^{2}$ . The area is $4\pi$ .

Finally, the surface area consists of the area of two circles and the area of the mid-section of the cylinder: $2\cdot 4\pi +4\pi h=16\pi$ , where $h$ is the height of the cylinder.

Thus, $h=2$ and the volume of the cylinder is $4\pi h=4\pi \cdot 2=8\pi$ .

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Example Question #101 : Solid Geometry

What is the volume of a cylinder that has a base with a radius of 5 and a height of 52?

Possible Answers:

1300

$77\pi$

$1300\pi$

230

Correct answer:

$1300\pi$

Explanation:

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is $Volume\:of\:cylinder= r^{2}*\pi*height\:of\:cylinder$

In this example the height is 52 and the radius is 5 which we plug into our equation which will look like this $Volume\:of\:cylinder= 5^{2}*\pi*52$

We then square the 5 to get $Volume=25*\pi*52$

Then perform multiplication to get $Volume=1300\pi$

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Example Question #641 : Geometry

What is the surface area of a cylinder with a radius of 2 cm and a height of 10 cm?

Possible Answers:

40π cm²

32π cm²

36π cm²

56π cm²

48π cm²

Correct answer:

48π cm²

Explanation:

SA_cylinder = 2πrh + 2πr² = 2π(2)(10) + 2π(2)² = 40π + 8π = 48π cm²

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Example Question #102 : Solid Geometry

A cylinder has a radius of r=3cm and a height of h=27cm . What is its volume?

Possible Answers:

$243\pi cm^{3}$

$\dpi{100} 234\pi cm^{3}$

$\dpi{100} 162\pi cm^{3}$

$\dpi{100} 81\pi cm^{3}$

$\dpi{100} 162\pi cm^{3}$

Correct answer:

$243\pi cm^{3}$

Explanation:

In order to calculate the volume of a cylinder, we must utilize the formula $V=\pi r^{2}h$ . We were given the radius, $\dpi{100} r=3cm$ , and the height, $\dpi{100} h=27cm$ .

Insert the known variables into the formula and solve for volume $\dpi{100} V$ .

$V=\pi *(3cm)^{2}*27cm$

$V=\pi*9cm^{2}*27cm$

$V=243\pi cm^{3}$

In essence, we find the area of the cylinder's circular base, $\dpi{100} A=\pi r^{2}$ , and multiply it by the height.

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Example Question #101 : Solid Geometry

A cylinder has a radius of $\dpi{100} r=\pi$ and a height of $\dpi{100} h=10$ . What is its volume

Possible Answers:

$10\pi^{3}$

$10\pi^{4}$

$10\pi^{2}$

Not enough information to solve.

$\sqrt{10\pi}$

Correct answer:

$10\pi^{3}$

Explanation:

In order to calculate the volume of a cylinder, we must utilize the formula $V=\pi r^{2}h$ . We were given the radius, $\dpi{100} \dpi{100} r=\pi$ , and the height, $\dpi{100} \dpi{100} h=10$ .

Insert the known variables into the formula and solve for volume $\dpi{100} V$ .

$\dpi{100} V=\pi *(\pi)^{2}*10$

$\dpi{100} V=\pi*\pi^{2}*10$

$\dpi{100} V=10\pi^{3}$

In essence, we find the area of the cylinder's circular base, $\dpi{100} A=\pi r^{2}$ , and multiply it by the height.

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

Cylinder_with_a_sphere

A sphere with a radius of r=2cm is circumscribed in a cylinder. What is the cylinder's volume?

Possible Answers:

$\dpi{100} 28.27cm^{3}$

$27.28cm^{3}$

$50.27cm^{3}$

$\dpi{100} 27.50cm^{3}$

Not enough information to solve

Correct answer:

$50.27cm^{3}$

Explanation:

In order to solve this problem, one key fact needs to be understood. A sphere will take up exactly $\frac{2}{3}$ of the volume of a cylinder in which it is circumscribed. Therefore, if we find the volume of the sphere we can then solve for the volume of the cylinder.

First, we need to find the volume of the sphere.

$\dpi{100} V=\frac{4}{3}\pi (2cm)^{3}$

$\dpi{100} \dpi{100} V_{sphere}=10\frac{2}{3}\pi cm^{3}$

This equals $\frac{2}{3}$ of the volume of the cylinder. Therefore,

$\dpi{100} V_{cylinder}=\frac{3}{2}(10\frac{2}{3}\pi cm^{3})$

$\rightarrow 50.27cm^{3}$

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

Calculate the volume of a cylinder with a height of six, and a base with a radius of three.

Possible Answers:

$18\pi$

$54\pi$

Correct answer:

$54\pi$

Explanation:

The volume of a cylinder is give by the equation $\small V=\pi r^2h$ .

In this example, $\small h=6$ and $\small r=3$ .

$V=\pi(3)^2(6)$

$V=\pi(9)(6)=54\pi$

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

What is the volume of a cylinder with a circular side with a radius of and a length of ?

Possible Answers:

$168\pi$

$334\pi$

$588\pi$

$84\pi$

Correct answer:

$588\pi$

Explanation:

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is

In this example the length is and the radius is so our equation will look like this $V=(12)(\pi)(7^{2})$

We then square the to get $7^{2}=49$

Then perform multiplication to get $(49)(12)(\pi)=588\pi$

The answer is $588\pi$ .

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

The volume of a cylinder is $54\pi$ units cubed. If the cylinder's height is units, what is its radius?

Possible Answers:

units

Correct answer:

units

Explanation:

The formula for the volume of a cylinder is $V = \pi r^2 \times h$ , where is volume, is the radius of the cylinder, and is its height. Substituing the given information into this equation makes it possible to find the radius by solving for :

$V = \pi r^2 \times h$

$\rightarrow 54\pi = \pi r^2 \times 6$

$\rightarrow \frac{54\pi}{6\pi} = \frac{(\pi r^2 \times 6)}{6\pi}$

$\rightarrow 9 = r^2$

$\rightarrow r = 3$ units

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

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

What is the volume of the right cylinder (m³)?

Possible Answers:

62.83

150.80

25.13

125.71

125.66

Correct answer:

125.71

Explanation:

The formula for the volume of a right cylinder is $\pi r^{2}h$ where is the radius and is the height. Thus for this problem

$\pi\cdot2^{2}\cdot10=125.71$

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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 #2 : How To Find The Volume Of A Cylinder

Example Question #101 : Solid Geometry

Example Question #641 : Geometry

Example Question #102 : Solid Geometry

Example Question #101 : Solid Geometry

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

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

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

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

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

All High School Math Resources

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