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GED Math : Area of a Circle

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Example Questions

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Example Question #131 : Geometry And Graphs

Find the area of a circle with a diameter of 18.

Possible Answers:

$108\pi$

$18\pi$

$324\pi$

$162\pi$

$81\pi$

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 $\frac{18}{2} = 9$ .

Substitute the radius.

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

The answer is: $81\pi$

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Example Question #131 : Geometry And Graphs

Find the area of a circle with a radius of 2x+1 .

Possible Answers:

4x^2+4x +1

$4\pi x^2+1$

$4\pi x^2+\pi$

$4\pi x^2+4\pi x +1$

$4\pi x^2+4\pi x +\pi$

Correct answer:

$4\pi x^2+4\pi x +\pi$

Explanation:

Write the formula for the area of a circle.

$A =\pi r^2$

Substitute the radius.

$A =\pi (2x+1)^2 = (2x+1) (2x+1) \pi$

Use the FOIL method to simplify the binomials.

(2x+1) (2x+1) = (2x)(2x) + (2x)(1) + (1)(2x)+(1)(1)

Simplify the terms.

4x^2+2x+2x+1 = 4x^2+4x +1

Multiply this quantity by pi.

$\pi (4x^2+4x +1)$

The answer is: $4\pi x^2+4\pi x +\pi$

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Example Question #43 : Area Of A Circle

Find the area of a circle with a radius of $3\pi ^8$ .

Possible Answers:

$9\pi^{64}$

$9\pi^{17}$

$9\pi^{16}$

$9\pi^{65}$

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

Correct answer:

$9\pi^{17}$

Explanation:

Write the formula for the area of a circle.

$A= \pi r^2$

Substitute the radius into the equation.

$A= \pi (3\pi ^8)^2= \pi (3\pi ^8)(3\pi ^8)$

The answer is: $9\pi^{17}$

Report an Error

Example Question #41 : Area Of A Circle

Find the area of a circle with a radius of 25.

Possible Answers:

$525\pi$

$150\pi$

$625 \pi$

$50\pi$

$125\pi$

Correct answer:

$625 \pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (25)^2 = \pi (25)(25) = 625 \pi$

The answer is: $625 \pi$

Report an Error

Example Question #141 : 2 Dimensional Geometry

Determine the area of a circle with a radius of .

Possible Answers:

$1600\pi$

$140\pi$

$40\pi$

$400 \pi$

$40\pi$

Correct answer:

$400 \pi$

Explanation:

Write the formula for the area of a circle.

$A =\pi r^2$

Substitute the radius.

$A =\pi (20)^2$

The answer is: $400 \pi$

Report an Error

Example Question #46 : Area Of A Circle

Find the area of a circle with a radius of 7in.

Possible Answers:

$14\pi \text{ in}^2$

$49\pi \text{ in}^2$

$3.5\pi \text{ in}^2$

$28\pi \text{ in}^2$

$21\pi \text{ in}^2$

Correct answer:

$49\pi \text{ in}^2$

Explanation:

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

$A = \pi r^2$

where r is the radius of the circle.

Now, we know the radius of the circle is 7in. So, we can substitute. We get

$A = \pi \cdot (7\text{in})^2$

$A = \pi \cdot 49\text{in}^2$

$A = 49\pi \text{ in}^2$

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Example Question #47 : Area Of A Circle

Let $\pi = 3.14$

Find the area of a circle with a diameter of 8in.

Possible Answers:

$50.24\text{in}^2$

$25.12\text{in}^2$

$153.86\text{in}^2$

$100.48\text{in}^2$

$200.96\text{in}^2$

Correct answer:

$50.24\text{in}^2$

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 $\pi = 3.14$ . We know the diameter of the circle is 8in. We know the diameter is two times the radius. Therefore, the radius is 4in. So, we substitute. We get

$A = 3.14 \cdot(4\text{in})^2$

$A = 3.14 \cdot 16\text{in}^2$

$A = 50.24\text{in}^2$

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Example Question #48 : Area Of A Circle

Determine the area of a circle with a radius of $9\sqrt{2}$ .

Possible Answers:

162

$81\pi$

$162\pi$

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

Correct answer:

$162\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (9\sqrt{2})^2=\pi (9\sqrt{2})(9\sqrt{2}) = 81\cdot 2 \pi$

The answer is: $162\pi$

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Example Question #49 : Area Of A Circle

Find the area of a circle with a diameter of $\sqrt{5}$ .

Possible Answers:

$\frac{5}{4}\pi$

$\pi\sqrt{10}$

$\frac{5}{8}\pi$

$\pi\sqrt5$

$\frac{5}{2}\pi$

Correct answer:

$\frac{5}{4}\pi$

Explanation:

Write the formula for the area of the circle.

$A=\pi r^2$

The radius is half the diameter.

$r= \frac{d}{2} = \frac{\sqrt5}{2}$

Substitute the radius.

$A=\pi (\frac{\sqrt5}{2})^2 = \pi (\frac{\sqrt5}{2})(\frac{\sqrt5}{2})$

The answer is: $\frac{5}{4}\pi$

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Example Question #41 : Area Of A Circle

Find the area of a circle with a diameter of 16.

Possible Answers:

$32\pi$

$16\pi$

$64\pi$

$128\pi$

$96\pi$

Correct answer:

$64\pi$

Explanation:

Write the formula for the area of a circle.

$A = \pi r^2$

The radius of the circle is half the diameter, or 8.

Substitute the radius into the equation.

$A = \pi (8)^2 = 64\pi$

The answer is: $64\pi$

Report an Error

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GED Math : Area of a Circle

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #131 : Geometry And Graphs

Example Question #131 : Geometry And Graphs

Example Question #43 : Area Of A Circle

Example Question #41 : Area Of A Circle

Example Question #141 : 2 Dimensional Geometry

Example Question #46 : Area Of A Circle

Example Question #47 : Area Of A Circle

Example Question #48 : Area Of A Circle

Example Question #49 : Area Of A Circle

Example Question #41 : Area Of A Circle

All GED Math Resources

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