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High School Math : Solid Geometry

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

Example Questions

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:

$12\pi$

$48\pi$

$16\pi$

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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High School Math : Solid Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

All High School Math Resources

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