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GED Math : 3-Dimensional Geometry

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Example Questions

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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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Example Question #1581 : Ged Math

A cylinder has the following measurements:

Height: 8in
Diameter: 6in

Find the volume.

Possible Answers:

$72\pi \text{ in}^3$

$64\pi \text{ in}^3$

$16\pi \text{ in}^3$

$24\pi \text{ in}^3$

$48\pi \text{ in}^3$

Correct answer:

$72\pi \text{ in}^3$

Explanation:

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

$V = \pi r^2 h$

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

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

We know the height of the cylinder is 8in.

Knowing this, we can substitute. We get

$V = \pi \cdot (3\text{in})^2 \cdot 8\text{in}$

$V = \pi \cdot 9\text{in}^2 \cdot 8\text{in}$

$V = \pi \cdot 72\text{in}^3$

$V = 72\pi \text{ in}^3$

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Example Question #61 : 3 Dimensional Geometry

What is the volume of a cylinder with a base area of $\sqrt\pi$ and a height of ?

Possible Answers:

$3\sqrt{\pi}$

$3\pi$

$9\pi$

$9\sqrt{\pi}$

Correct answer:

$3\sqrt{\pi}$

Explanation:

Write the formula for the volume of the cylinder.

$V=\pi r^2h$

The base area is a circle, which is $\pi r^2$ , and the area is already given.

This means we can substitute the area into the formula as is.

$V=\sqrt{\pi}(3)$

The answer is: $3\sqrt{\pi}$

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Example Question #621 : Geometry And Graphs

Find the volume of a cylinder with a base diameter of 6, and a height of 7.

Possible Answers:

$42\pi$

$21\pi$

$63\pi$

$84\pi$

$126\pi$

Correct answer:

$63\pi$

Explanation:

Write the formula for the area of a cylinder.

$V=\pi r^2 h$

The radius is half the diameter, of three.

Substitute the known dimensions into the formula.

$V=\pi (3)^2 7 = \pi (9) 7 = 63\pi$

The answer is: $63\pi$

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Example Question #622 : Geometry And Graphs

Find the volume of a cylinder with a radius of 8, and a height of 20.

Possible Answers:

$320\pi$

$\frac{1280}{3}\pi$

$120\pi$

$640\pi$

$1280\pi$

Correct answer:

$1280\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Substitute the radius and height into the equation.

$V=\pi( 8)^2(20)= \pi( 64)(20)$

The answer is: $1280\pi$

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GED Math : 3-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

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

Example Question #1581 : Ged Math

Example Question #61 : 3 Dimensional Geometry

Example Question #621 : Geometry And Graphs

Example Question #622 : Geometry And Graphs

All GED Math Resources

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