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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #12 : Cylinders

Find the surface area of the given cylinder.

Possible Answers:

471.20

488.66

471.20

923.63

Correct answer:

923.63

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

$\text{Area of Bases}=2\pi r^2$

Next, find the lateral surface area, which is a rectangle:

$\text{Lateral Surface Area}=2\pi r h$

Add the two together to get the equation to find the surface area of a cylinder:

$\text{Surface Area of Cylinder}=2\pi r^2+2\pi r h$

Plug in the given height and radius to find the surface area.

$\text{Surface Area of Cylinder}=2\pi(7)^2+2\pi(7)(14)=294\pi=923.63$

Make sure to round to places after the decimal point.

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Example Question #1052 : Intermediate Geometry

Inscribed

The above diagram shows a sphere inscribed inside a cylinder.

The sphere has a surface area of 100. Give the surface area of the cylinder.

Possible Answers:

$66\frac{2}{3}$

100

$133\frac{1}{3}$

150

Correct answer:

150

Explanation:

Let be the radius of the sphere. Then the radius of the base of the cylinder is also , and the height of the cylinder is h = 2r .

The surface area of the cylinder is

$A_{1} = 2\pi r (r+h)$

which, after substituting, is

$A_{1} = 2\pi r (r+2r)$

$A_{1} =2 \pi r (3r)$

$A_{1} =2\cdot 3 \cdot \pi r \cdot r$

$A_{1} = 6 \pi r^{2}$

The surface area of the sphere is

$A_{2} = 4 \pi r^{2}$

Therefore, the ratio of the former to the latter is

$\frac{A_{1} }{A_{2}}= \frac{6 \pi r^{2}}{4\pi r^{2}} = \frac{6}{4} = \frac{3}{2}$

and

$A_{1} = \frac{3}{2} A_{2}$

That is, the cylinder has surface area $\frac{3}{2}$ that of the sphere. Therefore, this area is

$A_{1} = \frac{3}{2} \cdot 100 = 150$ .

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Example Question #11 : Cylinders

How many gallon cans of paint must be purchased in order to put a single coat of paint over the surface of a cylindrical water tank if the tank is 75 feet high and 25 feet in radius, and each gallon can of paint covers 350 square feet?

Assume that there is a side, a top, and a bottom to be painted.

Possible Answers:

Correct answer:

Explanation:

First, use the formula $A = 2\pi r (r+h)$ to find the surface area of the tank in feet.

$A = 2\pi r (r+h) =A = 2\pi \cdot 25 \cdot (25+75) \approx 15,708$

Now divide by 350, remembering to round up.

$15,708 \div 350 \approx 44.9$

45 cans of paint need to be purchased.

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

Given a cylinder with radius of 5cm and height of 10cm, what is the volume of the cylinder?

Possible Answers:

$300\pi\;cm^2$

$500\pi\;cm^2$

$250\pi \; cm^2$

$200\pi\; cm^2$

$100\pi\;cm^2$

Correct answer:

$250\pi \; cm^2$

Explanation:

The volume of a cylinder is given by $\pi r^2\cdot height$

Notice how the formula for the volume is defined as the area of a circle times the lateral height of the cylinder. It is as if we are taking little paper circles and stacking them one-by-one until we fill up the entire container.

Plugging in the numbers we get:

$\pi (5)^2\cdot 10 = 250\pi$ cm^2

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

The volume of a cylinder is $64\pi$ , what is its height?

Possible Answers:

Any positive rational number

Any positive real number

Correct answer:

Any positive real number

Explanation:

Because both the radius and height are unspecified, any real number could be it's height as long as an matching radius is also chosen. There is no restriction on the height or radius being rational.

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

What is the volume of a hollow cylinder with an outer diameter of $8\; in$ , an inner diameter of $2\; in$ and a length of $18\; in$ ?

Possible Answers:

$270\pi \; in^{3}$

$288\pi \; in^{3}$

$300\pi \; in^{3}$

$250\pi \; in^{3}$

$320\pi \; in^{3}$

Correct answer:

$270\pi \; in^{3}$

Explanation:

The general formula for the volume of a hollow cylinder is given by $V=\pi (r_{o}^{2}-r_{i}^{2})l$ where $r_{o}$ is the outer radius, $r_{i}$ is the inner radius, and is the length.

The question gives diameters and we need to convert them to radii by cutting the diameters in half. Remember, d=2r . So the equation to solve becomes:

$V=\pi (4^{2}-1^{2})18$ or $V=270\pi\; in^{3}$

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

Find the volume of the following right cylinder: Cylinder33

Possible Answers:

$14\pi \ in^{3}$

$80\pi \ in^{3}$

$160\pi \ in^{3}$ .

$40\pi \ in^{3}$

$400\pi \ in^{3}$

Correct answer:

$160\pi \ in^{3}$ .

Explanation:

The correct answer is $160\pi \ in^{3}$ .

The formula for volume of a cylinder is

$\pi r^{2} h$

r=4 and h=10

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Example Question #121 : Solid Geometry

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:

$\small 18\pi$

$\small 24\pi$

$\small 36\pi$

$\small 28\pi$

$\small 70\pi$

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 #2 : How To Find The Volume Of A Cylinder

A right cylinder has a diameter of $2\:in$ and a height of $10\:in$ . What is the volume of this cylinder?

Possible Answers:

$32\:in^3$

$10 \pi\: in ^3$

$20 \pi\: in^3$

$31.4\:in^2$

$40 \pi\: in^3$

Correct answer:

$10 \pi\: in ^3$

Explanation:

The formula to find the volume of a cylinder is: $V = \pi \cdot r^2 \cdot h$ , where is the radius of the cylinder and is the height of the cylinder.

A good point to start in this kind of a formula-based problem is to ask "What information do I have?" and "What information is missing that I need?"

In this case, the problem provides us with the height of the cylinder and its diameter. We have the component of the equation, but we're missing the component. Can we find out ? The answer is yes! Radius is half of diameter. So in this case, because the diameter is $2\:in$ , the radius must be $1\:in$ .

Now that we have and , we are ready to solve for the volume after substituting in those values.

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

$V = \pi \cdot (1)^2 \cdot 10$

$V = \pi \cdot \1 \cdot 10$

$V = 10 \pi\: in^3$

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Example Question #7 : How To Find The Volume Of A Cylinder

You have just bought a farm that includes a storage silo. You want to find the volume for the 20 foot tall silo in the shape of a cylinder. You measure the circumference of the silo, it is listed below.

$Circumference=10\pi\ ft$

Leave answer in terms of $\pi$ .

Possible Answers:

$500\pi\ ft^{3}$

$25\pi\ ft^{3}$

$2000\pi\ ft^{3}$

$166\frac{2}{3}\pi\ ft^{3}$

Correct answer:

$500\pi\ ft^{3}$

Explanation:

To find the volume of a cylinder we need to find the area of the base and then multiply that by the height. The base is in the shape of a circle so the formula is given below:

$V=\pi\ r^{2}\ h$

To find the radius of the base, we use what was found from the measurement for circumference of the base. We set the formula for circumference equal to the measured circumference given in the problem.

$2\pi\ (r)=10\pi$

From this we can solve to find that the radius =5. Which we can plug into the original Volume formula. With the given height of 20 ft.

$V=\pi\ 5^{2}\ (20)$

Simplifying will give us the volume of the cylinder.

$V=500\pi\ ft^{3}$

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #12 : Cylinders

Example Question #1052 : Intermediate Geometry

Example Question #11 : 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 #1 : How To Find The Volume Of A Cylinder

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

Example Question #121 : Solid Geometry

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

Example Question #7 : How To Find The Volume Of A Cylinder

All Intermediate Geometry Resources

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