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GED Math : Geometry and Graphs

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #131 : 2 Dimensional Geometry

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

Find the area of a circle with a diameter of 14cm.

Possible Answers:

$43.96\text{cm}^2$ $\displaystyle 43.96\text{cm}^2$

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

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

$87.92\text{cm}^2$ $\displaystyle 87.92\text{cm}^2$

$615.44\text{cm}^2$ $\displaystyle 615.44\text{cm}^2$

Correct answer:

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

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 14cm. We also know the diameter is two times the radius. Therefore, the radius is 7cm. So, we can substitute. We get

$A = 3.14 \cdot (7\text{cm})^2$ $\displaystyle A = 3.14 \cdot (7\text{cm})^2$

$A = 3.14 \cdot 49\text{cm}^2$ $\displaystyle A = 3.14 \cdot 49\text{cm}^2$

$A = 153.86\text{cm}^2$ $\displaystyle A = 153.86\text{cm}^2$

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Example Question #132 : 2 Dimensional Geometry

Find the area of a circle with a diameter of $10\pi$ $\displaystyle 10\pi$.

Possible Answers:

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

$\displaystyle 10$

$25\pi ^2$ $\displaystyle 25\pi ^2$

$100\pi^4$ $\displaystyle 100\pi^4$

$25\pi ^3$ $\displaystyle 25\pi ^3$

Correct answer:

$25\pi ^3$ $\displaystyle 25\pi ^3$

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. Multiply the radius by one half.

$10\pi \cdot \frac{1}{2} = 5\pi$ $\displaystyle 10\pi \cdot \frac{1}{2} = 5\pi$

Substitute the radius into the equation.

$A=\pi (5\pi)^2 = \pi (5\pi)(5\pi) = 25\pi ^3$ $\displaystyle A=\pi (5\pi)^2 = \pi (5\pi)(5\pi) = 25\pi ^3$

The answer is: $25\pi ^3$ $\displaystyle 25\pi ^3$

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Example Question #133 : 2 Dimensional Geometry

Determine the area of a circle with a diameter of $\frac{5}{3}$ $\displaystyle \frac{5}{3}$.

Possible Answers:

$\frac{25}{18}\pi$ $\displaystyle \frac{25}{18}\pi$

$\frac{100}{9}\pi$ $\displaystyle \frac{100}{9}\pi$

$\frac{5}{18}\pi$ $\displaystyle \frac{5}{18}\pi$

$\frac{25}{36}\pi$ $\displaystyle \frac{25}{36}\pi$

$\frac{25}{9}\pi$ $\displaystyle \frac{25}{9}\pi$

Correct answer:

$\frac{25}{36}\pi$ $\displaystyle \frac{25}{36}\pi$

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. Multiply the diameter by half.

$\frac{5}{3}\cdot \frac{1}{2} = \frac{5}{6}$ $\displaystyle \frac{5}{3}\cdot \frac{1}{2} = \frac{5}{6}$

Substitute the radius into the equation.

$A=\pi (\frac{5}{6})^2= \pi (\frac{5}{6})(\frac{5}{6}) = \frac{25}{36}\pi$ $\displaystyle A=\pi (\frac{5}{6})^2= \pi (\frac{5}{6})(\frac{5}{6}) = \frac{25}{36}\pi$

The answer is: $\frac{25}{36}\pi$ $\displaystyle \frac{25}{36}\pi$

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Example Question #131 : Circles

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

Possible Answers:

$144\pi^2$ $\displaystyle 144\pi^2$

$24\pi ^2$ $\displaystyle 24\pi ^2$

$24\pi$ $\displaystyle 24\pi$

$144\pi$ $\displaystyle 144\pi$

144 $\displaystyle 144$

Correct answer:

$144\pi$ $\displaystyle 144\pi$

Explanation:

Write the formula for the area of a circle.

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

Substitute the radius.

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

The answer is: $144\pi$ $\displaystyle 144\pi$

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Example Question #135 : 2 Dimensional Geometry

Find the area of the circle with a circumference of $20\pi$ $\displaystyle 20\pi$.

Possible Answers:

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

$200\pi$ $\displaystyle 200\pi$

$20\pi$ $\displaystyle 20\pi$

$100\pi$ $\displaystyle 100\pi$

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

Correct answer:

$100\pi$ $\displaystyle 100\pi$

Explanation:

Write the formula for the circumference of a circle.

$C = 2\pi r$ $\displaystyle C = 2\pi r$

Substitute the circumference into the equation.

$20\pi= 2\pi r$ $\displaystyle 20\pi= 2\pi r$

Divide both sides by $2\pi$ $\displaystyle 2\pi$.

$\frac{20\pi}{2\pi}= \frac{2\pi r}{2\pi}$ $\displaystyle \frac{20\pi}{2\pi}= \frac{2\pi r}{2\pi}$

r=10 $\displaystyle r=10$

Write the formula for the area of a circle.

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

Substitute the radius into the equation.

$A=\pi (10)^2 = 100\pi$ $\displaystyle A=\pi (10)^2 = 100\pi$

The answer is: $100\pi$ $\displaystyle 100\pi$

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Example Question #132 : 2 Dimensional Geometry

Find the area of a circle with a radius of $7\pi ^3$ $\displaystyle 7\pi ^3$.

Possible Answers:

$7\pi ^6$ $\displaystyle 7\pi ^6$

$49 \pi ^6$ $\displaystyle 49 \pi ^6$

$49 \pi ^7$ $\displaystyle 49 \pi ^7$

$14\pi ^6$ $\displaystyle 14\pi ^6$

$14\pi ^7$ $\displaystyle 14\pi ^7$

Correct answer:

$49 \pi ^7$ $\displaystyle 49 \pi ^7$

Explanation:

Write the formula for the area of a circle.

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

Substitute the radius into the formula.

$A = \pi (7\pi ^3)^2 = \pi (7\pi ^3)(7\pi ^3)$ $\displaystyle A = \pi (7\pi ^3)^2 = \pi (7\pi ^3)(7\pi ^3)$

The answer is: $49 \pi ^7$ $\displaystyle 49 \pi ^7$

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Example Question #137 : 2 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

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 #138 : 2 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

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 #139 : 2 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

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 #131 : Geometry And Graphs

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

Possible Answers:

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

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

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

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

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

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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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #131 : 2 Dimensional Geometry

Example Question #132 : 2 Dimensional Geometry

Example Question #133 : 2 Dimensional Geometry

Example Question #131 : Circles

Example Question #135 : 2 Dimensional Geometry

Example Question #132 : 2 Dimensional Geometry

Example Question #137 : 2 Dimensional Geometry

Example Question #138 : 2 Dimensional Geometry

Example Question #139 : 2 Dimensional Geometry

Example Question #131 : Geometry And Graphs

All GED Math Resources

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