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GED Math : Area of a Circle

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Example Questions

Example Question #131 : 2 Dimensional Geometry

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

Possible Answers:

$81\pi$ $\displaystyle 81\pi$

$162\pi$ $\displaystyle 162\pi$

$18\pi$ $\displaystyle 18\pi$

$324\pi$ $\displaystyle 324\pi$

$108\pi$ $\displaystyle 108\pi$

Correct answer:

$81\pi$ $\displaystyle 81\pi$

Explanation:

Write the formula for the area of a circle.

$A = \pi r^2$ $\displaystyle A = \pi r^2$

The radius is half the diameter, or $\frac{18}{2} = 9$ $\displaystyle \frac{18}{2} = 9$ .

Substitute the radius.

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

The answer is: $81\pi$ $\displaystyle 81\pi$

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Example Question #41 : Area Of A Circle

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Write the formula for the area of a circle.

$A =\pi r^2$ $\displaystyle A =\pi r^2$

Substitute the radius.

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

Use the FOIL method to simplify the binomials.

$\displaystyle (2x+1) (2x+1) = (2x)(2x) + (2x)(1) + (1)(2x)+(1)(1)$

Simplify the terms.

$\displaystyle 4x^2+2x+2x+1 = 4x^2+4x +1$

Multiply this quantity by pi.

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

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

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Example Question #41 : Area Of A Circle

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

Possible Answers:

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

$9\pi^{16}$ $\displaystyle 9\pi^{16}$

$9\pi^{65}$ $\displaystyle 9\pi^{65}$

$9\pi^{64}$ $\displaystyle 9\pi^{64}$

$9\pi^{17}$ $\displaystyle 9\pi^{17}$

Correct answer:

$9\pi^{17}$ $\displaystyle 9\pi^{17}$

Explanation:

Write the formula for the area of a circle.

$A= \pi r^2$ $\displaystyle A= \pi r^2$

Substitute the radius into the equation.

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

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

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Example Question #132 : Geometry And Graphs

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

Possible Answers:

$50\pi$ $\displaystyle 50\pi$

$150\pi$ $\displaystyle 150\pi$

$125\pi$ $\displaystyle 125\pi$

$525\pi$ $\displaystyle 525\pi$

$625 \pi$ $\displaystyle 625 \pi$

Correct answer:

$625 \pi$ $\displaystyle 625 \pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$ $\displaystyle A=\pi r^2$

Substitute the radius.

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

The answer is: $625 \pi$ $\displaystyle 625 \pi$

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Example Question #141 : 2 Dimensional Geometry

Determine the area of a circle with a radius of $\displaystyle 20$ .

Possible Answers:

$400 \pi$ $\displaystyle 400 \pi$

$40\pi$ $\displaystyle 40\pi$

$1600\pi$ $\displaystyle 1600\pi$

$140\pi$ $\displaystyle 140\pi$

Correct answer:

$400 \pi$ $\displaystyle 400 \pi$

Explanation:

Write the formula for the area of a circle.

$A =\pi r^2$ $\displaystyle A =\pi r^2$

Substitute the radius.

$A =\pi (20)^2$ $\displaystyle A =\pi (20)^2$

The answer is: $400 \pi$ $\displaystyle 400 \pi$

Report an Error

Example Question #1102 : Ged Math

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

$A = \pi r^2$ $\displaystyle A = \pi r^2$

where r is the radius of the circle.

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

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

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

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

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Example Question #47 : Area Of A Circle

Let $\pi = 3.14$ $\displaystyle \pi = 3.14$

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

Possible Answers:

$100.48\text{in}^2$ $\displaystyle 100.48\text{in}^2$

$25.12\text{in}^2$ $\displaystyle 25.12\text{in}^2$

$200.96\text{in}^2$ $\displaystyle 200.96\text{in}^2$

$50.24\text{in}^2$ $\displaystyle 50.24\text{in}^2$

$153.86\text{in}^2$ $\displaystyle 153.86\text{in}^2$

Correct answer:

$50.24\text{in}^2$ $\displaystyle 50.24\text{in}^2$

Explanation:

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

$A = \pi \cdot r^2$ $\displaystyle A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know $\pi = 3.14$ $\displaystyle \pi = 3.14$ . 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

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

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

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

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Example Question #141 : 2 Dimensional Geometry

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

Possible Answers:

$162\pi$ $\displaystyle 162\pi$

162 $\displaystyle 162$

$\displaystyle 81$

$81\pi$ $\displaystyle 81\pi$

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

Correct answer:

$162\pi$ $\displaystyle 162\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$ $\displaystyle A=\pi r^2$

Substitute the radius.

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

The answer is: $162\pi$ $\displaystyle 162\pi$

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Example Question #44 : Area Of A Circle

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

Possible Answers:

$\pi\sqrt{10}$ $\displaystyle \pi\sqrt{10}$

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

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

$\pi\sqrt5$ $\displaystyle \pi\sqrt5$

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

Correct answer:

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

Explanation:

Write the formula for the area of the circle.

$A=\pi r^2$ $\displaystyle A=\pi r^2$

The radius is half the diameter.

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

Substitute the radius.

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

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

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Example Question #41 : Area Of A Circle

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

Possible Answers:

$16\pi$ $\displaystyle 16\pi$

$64\pi$ $\displaystyle 64\pi$

$32\pi$ $\displaystyle 32\pi$

$96\pi$ $\displaystyle 96\pi$

$128\pi$ $\displaystyle 128\pi$

Correct answer:

$64\pi$ $\displaystyle 64\pi$

Explanation:

Write the formula for the area of a circle.

$A = \pi r^2$ $\displaystyle A = \pi r^2$

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

Substitute the radius into the equation.

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

The answer is: $64\pi$ $\displaystyle 64\pi$

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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 : 2 Dimensional Geometry

Example Question #41 : Area Of A Circle

Example Question #41 : Area Of A Circle

Example Question #132 : Geometry And Graphs

Example Question #141 : 2 Dimensional Geometry

Example Question #1102 : Ged Math

Example Question #47 : Area Of A Circle

Example Question #141 : 2 Dimensional Geometry

Example Question #44 : Area Of A Circle

Example Question #41 : Area Of A Circle

All GED Math Resources

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