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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 #26 : Cylinders

You are painting a water tank black. You are trying to find the surface area of the tank so you measure the height and diameter of the tank. The height is 2.5 meters, and diameter is 4 meters. What is the total surface area of the tank?

Possible Answers:

$10 \pi \; m^2$

$18 \pi \; m^2$

$42 \pi \; m^2$

$14 \pi \; m^2$

$8 \pi \; m^2$

Correct answer:

$18 \pi \; m^2$

Explanation:

To find the surface area of a cylinder we need to find the area of the circular top and bottom and the area of the rectangular (but rounded) side, then add them together. Lets start by finding the area of the circular ends to the cylinder, remember that we measured the diameter (d) and we need the radius (r) to find the area of a circle, the radius is half of the diameter:

$A = r^2\pi = 2^2 \pi = 4\pi \; m^2$ (area of one circle)

Don't forget that we have two circles on the cylinder that have this area:

$4\pi \; m^2 + 4\pi \; m^2 = 8\pi \; m^2$ (area for both circles)

Now we just need to find the area of rectangular side of the cylinder. To do this we will take the hieght of the cylinder, 2.5 m, and multiply by the circumference (C) of the circle (the width of the rectangular side of the cylinder).

$C = 2\pi r \; \text{or} \; C= d\pi = 4\pi \; cm$

So now that we know the circumference we can multiply by the cylinder height to find the area of the rectangular side:

$4\pi \; cm \times 2.5 \; cm = 10\pi \; cm^2$ (area for rectangular side)

Now just add to find the total surface area:

$8\pi \; cm^2 + 10\pi \; cm^2 = 18\pi \; cm^2$

and that is our total surface area for the cylinder!

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Example Question #27 : Cylinders

A can of tomato soup has a diameter of 3.5 inches and a height of 8 inches. What is the volume of the can of soup?

Possible Answers:

$14\pi \; cm^3$

$24.5\pi \; cm^3$

$12.25\pi \; cm^3$

$3.0625\pi \; cm^3$

$28\pi \; cm^3$

Correct answer:

$24.5\pi \; cm^3$

Explanation:

To find the volume of a soup can, or a cylinder, we use the formula for volume:

$\text {Base Area x Height = Volume}$

The base of our cylinder is a circle and to find the area of the circle we use:

$\text {Area =} \; \pi\times r^2 \;, \text {here our radius = }\frac{3.5}{2} = 1.75cm$

Now we can use the formula for the area of our circular base:

$\text {Area =} \; \pi\times (1.75)^2 = 3.0625\pi \; cm^2$

All we need to do now is multiply the base by the hieght of our cylinder!

$3.0625 \pi \; cm^2 \times 8cm = 24.5\pi \; cm^3$

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Example Question #10 : How To Find The Volume Of A Cylinder

Find the volume of a cylinder that has a radius of and a height of .

Possible Answers:

$8\pi$

$16\pi$

$24\pi$

$32\pi$

Correct answer:

$16\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 2^2\times 4$

Solve.

$\text{Volume of Cylinder}=16\pi$

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Example Question #101 : Solid Geometry

Find the volume of a cylinder that has a radius of and a height of .

Possible Answers:

$33\pi$

$27\pi$

$9\pi$

$81\pi$

Correct answer:

$27\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 3^2\times 3$

Solve.

$\text{Volume of Cylinder}=27\pi$

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Example Question #102 : Solid Geometry

Find the volume of a cylinder that has a radius of and a height of .

Possible Answers:

$64\pi$

$8\pi$

$16\pi$

$32\pi$

Correct answer:

$32\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 4^2\times 2$

Solve.

$\text{Volume of Cylinder}=32\pi$

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Example Question #103 : Solid Geometry

Find the volume of a cylinder that has a radius of and a height of .

Possible Answers:

$100\pi$

$50\pi$

$200\pi$

$75\pi$

Correct answer:

$100\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 5^2\times 4$

Solve.

$\text{Volume of Cylinder}=100\pi$

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Example Question #104 : Solid Geometry

Find the volume of a cylinder that has a radius of $\frac{1}{2}$ and a height of .

Possible Answers:

$\pi$

$2\pi$

$4\pi$

$8\pi$

Correct answer:

$2\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times\left( \frac{1}{2}\right)^2\times 8$

Solve.

$\text{Volume of Cylinder}=2\pi$

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Example Question #105 : Solid Geometry

Find the volume of a cylinder that has a radius of and a height of .

Possible Answers:

$144\pi$

$36\pi$

$72\pi$

$48\pi$

Correct answer:

$72\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 6^2\times 2$

Solve.

$\text{Volume of Cylinder}=72\pi$

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Example Question #106 : Solid Geometry

Find the volume of a cylinder that has a radius of and a height of .

Possible Answers:

$75\pi$

$2025\pi$

$1775\pi$

$1225\pi$

Correct answer:

$2025\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 15^2\times 9$

Solve.

$\text{Volume of Cylinder}=2025\pi$

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Example Question #107 : Solid Geometry

Find the volume of a cylinder that has a radius of $\frac{1}{4}$ and a height of .

Possible Answers:

$\sqrt3\pi$

$6\pi$

$3\pi$

$9\pi$

Correct answer:

$3\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times \left(\frac{1}{4}\right)^2\times 48$

Solve.

$\text{Volume of Cylinder}=3\pi$

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #26 : Cylinders

Example Question #27 : Cylinders

Example Question #10 : How To Find The Volume Of A Cylinder

Example Question #101 : Solid Geometry

Example Question #102 : Solid Geometry

Example Question #103 : Solid Geometry

Example Question #104 : Solid Geometry

Example Question #105 : Solid Geometry

Example Question #106 : Solid Geometry

Example Question #107 : Solid Geometry

All Intermediate Geometry Resources

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