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GED Math : Volume of a Cylinder

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Example Question #11 : Volume Of A Cylinder

If the circular base area of a cylinder is , what is the volume of the cylinder if the height is ?

Possible Answers:

$250\pi$

$50\pi$

$500\pi$

Correct answer:

Explanation:

Write the formula for the volume of the cylinder.

$V=\pi r^2 h$

The area of the circle is $A =\pi r^2$ .

We can replace this term with .

Substitute the known terms.

$V=(\pi r^2 )h = (10)(5) = 50$

The volume is:

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Example Question #51 : 3 Dimensional Geometry

Find the volume of a cylinder with the following measurements:

Diameter: 8in

Height: 12in

Possible Answers:

$192\pi \text{ in}^3$

$144\pi \text{ in}^3$

$768\pi \text{ in}^3$

$96\pi \text{ in}^3$

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

Correct answer:

$192\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

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

where r is the radius, and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 8in. We also know the diameter is two times the radius. Therefore, the radius is 4in.

We know the height of the cylinder is 12in.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot (4\text{in})^2 \cdot 12\text{in}$

$V = \pi \cdot 16\text{in}^2 \cdot 12\text{in}$

$V = \pi \cdot 192\text{in}^3$

$V = 192\pi \text{ in}^3$

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Example Question #13 : Volume Of A Cylinder

Find the volume of a cylinder with a height of 14in and a diameter of 8in.

Possible Answers:

$56\pi \text{ in}^3$

$224\pi \text{ in}^3$

$392\pi \text{ in}^3$

$112\pi \text{ in}^3$

$196\pi \text{ in}^3$

Correct answer:

$224\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the formula

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

where r is the radius, and h is the height of the cylinder.

Now, we know the height of the cylinder is 14in.

We know the diameter of the cylinder is 8in. We also know the diameter is two times the radius. Therefore, the radius is 4in.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot (4\text{in})^2 \cdot 14\text{in}$

$V = \pi \cdot 16\text{in}^2 \cdot 14\text{in}$

$V = \pi \cdot 224\text{in}^3$

$V = 224\pi \text{ in}^3$

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Example Question #14 : Volume Of A Cylinder

What is the volume of a cylinder if the base diameter is 10, and the height is 5?

Possible Answers:

$100\pi$

$\textup{The answer is not given.}$

$125 \pi$

$500\pi$

$250\pi$

Correct answer:

$125 \pi$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

The radius is half the diameter.

Substitute the terms in the equation.

$V=\pi5^2(5) = 125 \pi$

The answer is: $125 \pi$

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Example Question #61 : 3 Dimensional Geometry

Find the volume of a cylinder with a base area of 6 and a height of 4.

Possible Answers:

$48\pi$

$144\pi$

144

Correct answer:

Explanation:

The base of the cylinder is a circle, and the area of the base is already given.

Write the volume of the cylinder.

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

Substitute the known values to determine the volume.

V=6(4) = 24

The volume is:

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Example Question #16 : Volume Of A Cylinder

What is the volume of a cylinder with a base circumference of $2\pi$ and a height of ?

Possible Answers:

$8\pi$

$16\pi^2$

$5\pi$

$32\pi^2$

$4\pi$

Correct answer:

$4\pi$

Explanation:

To determine the radius of the base, write the circumference formula. The base represents a circle.

$C=2\pi r$

Substitute the circumference.

$2\pi =2\pi r$

Divide by $2\pi$ on both sides.

$\frac{2\pi}{2\pi} =\frac{2\pi r}{2\pi}$

r=1

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Substitute the radius and height.

$V=\pi (1)^2(4) = 4\pi$

The answer is: $4\pi$

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Example Question #17 : Volume Of A Cylinder

Find the volume of a cylinder with the following measurements:

Diameter: 10in

Height: 14in

Possible Answers:

$70\pi \text{ in}^3$

$490\pi \text{ in}^3$

$140\pi \text{ in}^3$

$350\pi \text{ in}^3$

$280\pi \text{ in}^3$

Correct answer:

$350\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

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

where r is the radius, and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 10in. We also know the diameter is two times the radius. Therefore, the radius is 5in.

We know the height of the cylinder is 14in.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot (5\text{in})^2 \cdot 14\text{in}$

$V = \pi \cdot 25\text{in}^2 \cdot 14\text{in}$

$V = \pi \cdot 350\text{in}^3$

$V = 350\pi \text{ in}^3$

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Example Question #11 : Volume Of A Cylinder

Find the volume of a cylinder with a height of 11in and a diameter of 6in.

Possible Answers:

$127\pi \text{ in}^3$

$45\pi \text{ in}^3$

$99\pi \text{ in}^3$

$67\pi \text{ in}^3$

$66\pi \text{ in}^3$

Correct answer:

$99\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the formula

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

where r is the radius, and h is the height of the cylinder.

Now, we know the height of the cylinder is 11in.

We know the diameter of the cylinder is 6in. We also know the diameter is two times the radius. Therefore, the radius is 3in.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot (3\text{in})^2 \cdot 11\text{in}$

$V = \pi \cdot 9\text{in}^2 \cdot 11\text{in}$

$V = \pi \cdot 99\text{in}^3$

$V = 99\pi \text{ in}^3$

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Example Question #61 : 3 Dimensional Geometry

Determine the volume of a cylinder with a radius of 5, and a height of 20.

Possible Answers:

$1000\pi$

$250\pi$

$50\pi$

$500 \pi$

$100\pi$

Correct answer:

$500 \pi$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Substitute the radius and the height into the formula.

$V=\pi (5^2)(20) = \pi (25)(20) = 500 \pi$

The answer is: $500 \pi$

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Example Question #611 : Geometry And Graphs

Find the volume of a cylinder if the base area is 4, and the height is 15.

Possible Answers:

240

$240\pi$

$\textup{The answer is not given.}$

$60\pi$

Correct answer:

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

The base of a cylinder is a circle, and the area of the circle is $\pi r^2$ .

This means that we can substitute the base area into the term $\pi r^2$ .

$V=(\pi r^2)h = 4(15) = 60$

The answer is:

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GED Math : Volume of a Cylinder

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : Volume Of A Cylinder

Example Question #51 : 3 Dimensional Geometry

Example Question #13 : Volume Of A Cylinder

Example Question #14 : Volume Of A Cylinder

Example Question #61 : 3 Dimensional Geometry

Example Question #16 : Volume Of A Cylinder

Example Question #17 : Volume Of A Cylinder

Example Question #11 : Volume Of A Cylinder

Example Question #61 : 3 Dimensional Geometry

Example Question #611 : Geometry And Graphs

All GED Math Resources

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