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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 #54 : Area Of A Circle

Find the area of a circle if the radius is $2\sqrt2$ .

Possible Answers:

$8\pi$

$4\pi$

$6\pi$

$12\pi$

$16\pi$

Correct answer:

$8\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the formula.

Remember when squaring the radius, square both terms. Also recall that when two square roots that have the same base are multiplied together, the square root sign disappears and you are left with the number underneath the square root sign.

$(2\sqrt{2})^2=2^2\cdot \sqrt2\cdot \sqrt2=4\cdot 2$

Therefore the area becomes,

$A=\pi (2\sqrt2)^2 = \pi (4\times 2) = 8\pi$ .

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Example Question #55 : Area Of A Circle

Find the area of a circle if the circle has a perimeter of .

Possible Answers:

$18\pi$

$\frac{9}{\pi}$

$6\pi$

$36\pi$

$\frac{6}{\pi}$

Correct answer:

$\frac{9}{\pi}$

Explanation:

The circle's perimeter is the same as the circle's circumference.

Write the circumference formula for the circle.

$C=2\pi r$

Substitute the circumference and solve for the radius.

$6=2\pi r$

$r=\frac{3}{\pi}$

Write the formula for the area of a circle.

$A=\pi r^2$

$A=\pi (\frac{3}{\pi})^2 = \pi (\frac{9}{\pi^2}) =\frac{9}{\pi}$

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Example Question #56 : Area Of A Circle

Suppose the circle is inscribed inside a square touching all four sides of the square. The side length of the square is 2. What is the area of the circle?

Possible Answers:

$\frac{\pi}{2}$

$2\pi$

$\sqrt2 \pi$

$\pi$

$4\pi$

Correct answer:

$\pi$

Explanation:

Since the side of the square is 2, the diameter of the circle must also be 2. The radius of the circle is half the diameter, which would be 1.

Write the formula for the area of the circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi r^2 = \pi (1)^2 = \pi$

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Example Question #54 : Area Of A Circle

Solve for the area of a circle if the radius is .

Possible Answers:

$4\pi + \pi x^2$

$4\pi x$

$4\pi^2 x^2$

4+x^2

$4\pi x^2$

Correct answer:

$4\pi x^2$

Explanation:

Write the formula to find the area of a circle.

$A=\pi r^2$

Substitute the radius.

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

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Example Question #58 : Area Of A Circle

Find the area of a circle with a diameter of .

Possible Answers:

$\frac{\pi x^2}{4}$

$\pi x^2$

$4\pi x^2$

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

$2\pi x^2$

Correct answer:

$\frac{\pi x^2}{4}$

Explanation:

Write the area of the circle.

$A=\pi r^2$

The radius is half the diameter.

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

Substitute the radius into the area formula.

Remember that when a fraction is squared, both the numerator and denominator are squared.

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

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Example Question #59 : Area Of A Circle

Solve for the area of the circle if the circumference is $16\pi$ .

Possible Answers:

$256\pi$

$96\pi$

$16\pi$

$64\pi$

$8\pi$

Correct answer:

$64\pi$

Explanation:

Write the formula for the circumference of a circle to find the radius.

$C=2\pi r$

$16\pi=2\pi r$

Divide by $2\pi$ on both sides of the equation.

$\frac{16\pi}{2\pi}=\frac{2\pi r}{2\pi}$

$\frac{2\pi \times 8}{2\pi}=\frac{2\pi r}{2\pi}$

Cancel out the $2\pi$ in the numerator and denominator. The radius is:

r=8

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius and find the area.

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

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Example Question #172 : Geometry

Find the area of a circle if the radius is $\sqrt7$ .

Possible Answers:

$\sqrt{7\pi}$

$7\pi$

$49\pi$

$\pi\sqrt7$

$\sqrt{\pi+7}$

Correct answer:

$7\pi$

Explanation:

Write the formula to find the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (\sqrt7)^2$

When a square root is squared, the square root is eliminated.

$(\sqrt x)^2 = (\sqrt x)(\sqrt x)=x$

Expand the terms.

$A=\pi (\sqrt7)^2 = \pi (\sqrt7)(\sqrt7) = 7\pi$

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Example Question #61 : Area Of A Circle

Solve for the area of a circle with a radius of 9.

Possible Answers:

$36\pi$

$18\pi$

$324\pi$

$81\pi$

$27\pi$

Correct answer:

$81\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the length of the radius into the equation.

$A=\pi (9)^2$

Expand and simplify.

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

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Example Question #172 : Area

Solve for the area of a circle if the perimeter of the circle is $10\pi$ .

Possible Answers:

$10\pi$

$25\pi$

$50\pi$

$100\pi$

$2\pi$

Correct answer:

$25\pi$

Explanation:

The perimeter is similar to the circle's circumference.

Write the circumference formula.

$C=2\pi r$

Substitute the circumference to find the radius.

$10\pi=2\pi r$

Divide by $2\pi$ on both sides of the equation.

$\frac{10\pi}{2\pi}=\frac{2\pi r}{2\pi}$

r=5

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi r^2 = \pi (5)^2= 25\pi$

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Example Question #173 : Area

Determine the area of a circle with a diameter of five.

Possible Answers:

$25\pi$

$\frac{25}{4}\pi$

$\frac{25\pi}{2}$

$12\pi$

$10\pi$

Correct answer:

$\frac{25}{4}\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Divide the diameter by two to get the radius.

$r=\frac{d}{2} = \frac{5}{2}$

Substitute the radius. Expand the fraction and multiply the numerator by the numerator, and the denominator with the denominator.

$A=\pi (\frac{5}{2})^2 = \pi (\frac{5}{2})(\frac{5}{2}) = \frac{25}{4}\pi$

The area of the circle is: $\frac{25}{4}\pi$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #54 : Area Of A Circle

Example Question #55 : Area Of A Circle

Example Question #56 : Area Of A Circle

Example Question #54 : Area Of A Circle

Example Question #58 : Area Of A Circle

Example Question #59 : Area Of A Circle

Example Question #172 : Geometry

Example Question #61 : Area Of A Circle

Example Question #172 : Area

Example Question #173 : Area

All Pre-Algebra Resources

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