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High School Math : Geometry

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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:

$12\pi$

$48\pi$

$16\pi$

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:

$9 \pi$

$12 \pi$

$18 \pi$

$24 \pi$

$36 \pi$

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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Example Question #23 : Cylinders

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:

$8\pi$

$10\pi$

$4\pi$

$6\pi$

$2\pi$

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 #1 : How To Find The Volume Of A Cylinder

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

Possible Answers:

230

$1300\pi$

$77\pi$

1300

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 #1 : How To Find The Volume Of A Cylinder

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

Possible Answers:

56π cm²

32π cm²

40π cm²

48π cm²

36π 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 #3 : How To Find The Volume Of A Cylinder

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

Possible Answers:

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

$243\pi cm^{3}$

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

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

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 #4 : How To Find The Volume Of A Cylinder

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

Possible Answers:

Not enough information to solve.

$\sqrt{10\pi}$

$10\pi^{2}$

$10\pi^{3}$

$10\pi^{4}$

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 #5 : 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:

$27.28cm^{3}$

Not enough information to solve

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

$50.27cm^{3}$

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

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 #1 : 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:

$54\pi$

$18\pi$

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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High School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Cylinders

Example Question #1 : Cylinders

Example Question #1 : Cylinders

Example Question #23 : Cylinders

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

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

Example Question #3 : How To Find The Volume Of A Cylinder

Example Question #4 : How To Find The Volume Of A Cylinder

Example Question #5 : How To Find The Volume Of A Cylinder

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

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