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GED Math : GED Math

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Example Questions

Example Question #91 : 2 Dimensional Geometry

Use 3.14 for pi.

What is the circumference of a circle with a radius of 21cm?

Possible Answers:

131.88cm

$131.88cm^{2}$

65.94cm

$65.94cm^{2}$

$1384.74cm^{2}$

Correct answer:

131.88cm

Explanation:

First we need to recognize that we are given the length of the radius which is 21 cm. We need to know that the diameter of a circle is twice the length of the radius, so our diameter is 42cm.

Now we need to recall the formula for circumference of a circle:

$Circumference=D\cdot \pi$

Where is diameter.

We can plug in 42cm for our diameter and use 3.14 for pie

$Circumference=42cm\cdot3.14$

Then we multiply

Circumference= 131.88cm

Notice our answer remains in centimeters

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Example Question #1 : Area Of A Circle

A circular swimming pool at an apartment complex has diameter 50 feet. The apartment manager needs to purchase a tarp that will cover this pool completely, but the store will only sell the material in multiples of ten square yards. How many square yards will the manager need to buy?

Use 3.14 for $\pi$ .

Possible Answers:

$210 \textrm{ yd}^{2}$

$160 \textrm{ yd}^{2}$

$150 \textrm{ yd}^{2}$

$220 \textrm{ yd}^{2}$

Correct answer:

$220 \textrm{ yd}^{2}$

Explanation:

The radius of the swimming pool is half the diameter, or 25 feet.

The area of the swimming pool is $\pi$ times the square of the radius, or

$\pi \times 25 ^{2} = 3.14 \times 625 = 1,962.5$ square feet, or

$1,962.5 \div 9 \approx 218$ square yards.

The manager will need to buy a number of square yards of tarp equal to the next highest multiple of ten, which is 220 square yards.

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Example Question #1 : Area Of A Circle

A circular swimming pool at an apartment complex has diameter 30 meters. The apartment manager needs to purchase a tarp that will cover this pool completely, but the store will only sell the material in multiples of ten square meters. How many square yards will the manager need to buy?

Use 3.14 for $\pi$ .

Possible Answers:

$700 \textrm{ m}^{2}$

$710 \textrm{ m}^{2}$

$100 \textrm{ m}^{2}$

$110 \textrm{ m}^{2}$

Correct answer:

$710 \textrm{ m}^{2}$

Explanation:

The radius of the swimming pool is half the diameter, or 15 meters.

The area of the swimming pool is $\pi$ times the square of the radius, or

$\pi \times 15 ^{2} = 3.14 \times 225 = 706.5$ square meters.

The manager will need to buy a number of square yards of tarp equal to the next highest multiple of ten, which is 710 square meters.

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Example Question #2 : Area Of A Circle

Axes_1

Give the circumference of the above circle. Assume each mark on each axis represents one unit.

Possible Answers:

$10 \pi$

$25 \pi$

$100 \pi$

$5 \pi$

Correct answer:

$10 \pi$

Explanation:

The diameter of the circle - the distance from one point to the opposite point - is 10 units, so the circumference is this multiplied by $\pi$ , or $10 \pi$ .

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Example Question #3 : Area Of A Circle

What is the area of a circle with a diameter of $12\pi$ ?

Possible Answers:

$12\pi^2$

$144\pi$

$36\pi$

$144\pi^2$

$36\pi^3$

Correct answer:

$36\pi^3$

Explanation:

Be careful on several counts for this question. First, remember that you need the radius for calculating area. Therefore, since you know that the diameter is $12\pi$ , you can say that the radius is $6\pi$ .

Next, be very careful given that there is already a $\pi$ in your radius. The formula for the area of a circle is:

$A=\pi r^2$

For your data, this is:

$A=\pi (6\pi)^2=\pi * 36\pi^2=36\pi^3$

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Example Question #3 : Area Of A Circle

What is the area of the circle with a radius of 25?

Possible Answers:

$150\pi$

$125\pi$

$5\pi$

$250\pi$

$625 \pi$

Correct answer:

$625 \pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (25)^2$

Simplify the equation.

$A=\pi (25)(25) = 625 \pi$

The answer is: $625 \pi$

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Example Question #1 : Area Of A Circle

Find the area of a circle with a radius of 12.

Possible Answers:

$24\pi$

$144\pi$

$144\pi ^2$

$24\pi ^2$

$36\pi$

Correct answer:

$144\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (12)^2 = 144\pi$

The answer is: $144\pi$

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Example Question #1 : Area Of A Circle

What is the area of a circle with the diameter of 18?

Possible Answers:

$343\pi$

$36\pi$

$324 \pi$

$432\pi$

$81\pi$

Correct answer:

$81\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

The radius is half the diameter, or 9.

Substitute the value of the radius in to the formula.

$A=\pi( 9)^2 = 81\pi$

The answer is: $81\pi$

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Example Question #4 : Area Of A Circle

Find the area of a circle with a radius of $2\pi$ .

Possible Answers:

$2\pi ^2$

$2\pi ^3$

$4\pi ^3$

$4\pi$

$4\pi ^2$

Correct answer:

$4\pi ^3$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (2\pi)^2$

Simplify this equation.

$A=\pi (2\pi)(2\pi) = 4\pi ^3$

The answer is: $4\pi ^3$

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Example Question #5 : Area Of A Circle

Find the area of a circle with a diameter of 22cm.

Possible Answers:

$88\pi \text{ cm}^2$

$121\pi \text{ cm}^2$

$100\pi \text{ cm}^2$

$144\pi \text{ cm}^2$

$44\pi \text{ cm}^2$

Correct answer:

$121\pi \text{ cm}^2$

Explanation:

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know the diameter of the circle is 22cm. We also know the diameter is two times the radius. Therefore, the radius is 11cm.

So, we can substitute. We get

$A = \pi \cdot (11\text{cm})^2$

$A = \pi \cdot 121\text{cm}^2$

$A = 121\pi \text{ cm}^2$

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #91 : 2 Dimensional Geometry

Example Question #1 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #2 : Area Of A Circle

Example Question #3 : Area Of A Circle

Example Question #3 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #4 : Area Of A Circle

Example Question #5 : Area Of A Circle

All GED Math Resources

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