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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #161 : Area

Find the area of a circle with a radius of $\frac{2}{7}$ .

Possible Answers:

$\frac{49}{4}$

$\frac{4}{49}\pi$

$\frac{\pi}{49}$

$\frac{4}{49}$

$\frac{4}{7}\pi$

Correct answer:

$\frac{4}{49}\pi$

Explanation:

Write the formula for area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (\frac{2}{7})^2 = \frac{4}{49}\pi$

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Example Question #162 : Area

Find the area of a circle with the diameter of $\frac{1}{10}$ .

Possible Answers:

$\frac{\pi}{100}$

$\frac{\pi}{50}$

$\frac{\pi}{200}$

$\frac{\pi}{25}$

$\frac{\pi}{400}$

Correct answer:

$\frac{\pi}{400}$

Explanation:

Write the formula to find the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

$r=\frac{1}{2}d = \frac{1}{2} \times \frac{1}{10} = \frac{1}{20}$

Substitute the radius into the formula.

$A=\pi( \frac{1}{20})^2 = \frac{\pi}{400}$

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Example Question #46 : Area Of A Circle

The diameter of a circle is 21. Which of the following is the closest area?

Possible Answers:

132

1385

350

Correct answer:

350

Explanation:

Divide the diameter by two to obtain the radius.

$r=\frac{d}{2} = \frac{21}{2} = 10.5$

Write the area of a circle.

$A=\pi r^2$

Substitute the radius and solve. Assume $\pi = 3.14$ .

A=(3.14)(10.5)^2 = 346.185

The rounded answer is 350 .

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Example Question #47 : Area Of A Circle

Find the area of a circle with a circumference of $18\pi$ .

Possible Answers:

$324\pi$

$162\pi$

$36\pi$

$81\pi$

$9\pi$

Correct answer:

$81\pi$

Explanation:

Write the circumference formula and substitute the circumference.

$C=2\pi r$

$18\pi =2\pi r$

Now solve for r by dividing $2\pi$ on each side.

r=9

Write the formula to find the area of a circle.

$A=\pi r^2$

Since we solved for the radius in the above calculation, we will substitute that found value into the area formula and solve.

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

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Example Question #41 : Area Of A Circle

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

Possible Answers:

$36\pi$

$18\pi$

$144\pi$

144

Correct answer:

$36\pi$

Explanation:

First identify the relationship between diameter and radius of a circle. Then, divide the diameter by two to get the radius.

$r=\frac{d}{2}= \frac{12}{2}=6$

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (6)^2$

$A=36\pi$

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Example Question #49 : Area Of A Circle

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

Possible Answers:

$\frac{\pi^3}{4}$

$\pi^3$

$\frac{\pi^2}{2}$

$\frac{\pi^3}{2}$

$\frac{\pi^2}{2}$

Correct answer:

$\frac{\pi^3}{4}$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

To obtain the radius, divide the diameter by

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

Substitute the radius into the area.

$A=\pi \left (\frac{\pi}{2} \right )^2 = \frac{\pi^3}{4}$

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Example Question #50 : Area Of A Circle

Find the area of a circle in $\textup{feet}$ if the radius is $2 \textup{ inches}$ .

Possible Answers:

$4\pi\textup{ feet}$

$\frac{\pi}{36}\textup{ feet}$

$\frac{\pi}{96}\textup{ feet}$

$\frac{\pi}{12}\textup{ feet}$

$36\pi\textup{ feet}$

Correct answer:

$\frac{\pi}{36}\textup{ feet}$

Explanation:

Convert $\textup{2 inches}$ to $\textup{feet}$ . There are $\textup{12 inches}$ in a foot.

$r= 2 \textup{ inches }(\frac{1 \textup{ foot}}{12 \textup{ inches }}) = \frac{1}{6} \textup{ foot}$

Write the formula for area of a circle and substitute the new radius.

$A=\pi r^2 = \pi (\frac{1}{6})^2 =\frac{\pi}{36}\textup{ feet}$

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Example Question #51 : Area Of A Circle

Determine the area of a circle with a radius of $4\pi$ .

Possible Answers:

$16\pi^2$

$16\pi^3$

$4\pi^4$

$4\pi^2$

$4\pi^3$

Correct answer:

$16\pi^3$

Explanation:

Write the equation to find the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (4\pi)^2 = \pi (16\pi^2) = 16\pi^3$

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Example Question #52 : Area Of A Circle

Find the area of a circle if the radius is 24.

Possible Answers:

$48\pi$

$576 \pi$

$288\pi$

$72\pi$

$144\pi$

Correct answer:

$576 \pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

When multiplying two digit numbers together remember to do it in steps.

$24\\ \underline{\times\ 24}$

First multiply $4\times 4=16$ , the six will stay in the ones place and the one will be carried to the tens place above the two.

${\color{Red} 2}4\\ \underline{\times\ 2{\color{Red} 4}}$

Now multiply four and the two (highlighted in red above) then add the one that was carried over.

$2\times 4=8+1=9$

This number goes next to the six.

$2{\color{Red}4}\\ \underline{\times\ {\color{Red} 2}4}$

Placing a zero in the ones places signifies that we are in our second step of multiplication. We will multiply the two and four (highlighted in red).

$2{\color{Red}4}\\ \underline{\times\ {\color{Red} 2}4}$

Now we will multiply two and two,

${\color{Red}2}4\\ \underline{\times\ {\color{Red} 2}4}$

480

From here add down to get the final product.

96+480=576

Therefore the final area is,

$A=\pi (24)^2 =576 \pi$ .

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Example Question #53 : Area Of A Circle

Find the area of the circle if the radius is .

Possible Answers:

$25\pi$

$250\pi$

$100\pi$

$15625\pi$

$2500\pi$

Correct answer:

$2500\pi$

Explanation:

Substitute the radius into the formula for the area of a circle.

$A=\pi r^2 = \pi (50 )^2 = 2500\pi$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #161 : Area

Example Question #162 : Area

Example Question #46 : Area Of A Circle

Example Question #47 : Area Of A Circle

Example Question #41 : Area Of A Circle

Example Question #49 : Area Of A Circle

Example Question #50 : Area Of A Circle

Example Question #51 : Area Of A Circle

Example Question #52 : Area Of A Circle

Example Question #53 : Area Of A Circle

All Pre-Algebra Resources

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