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Pre-Algebra : Area of a Circle

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Example Questions

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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Example Question #62 : Area Of A Circle

Find the area of the circle with the radius of x-10 .

Possible Answers:

$x^2\pi-20x\pi+100\pi$

$2x^2\pi - 20x\pi$

$x^2\pi^2-20x\pi^2+100\pi^2$

$x^2\pi -100\pi$

$x^2\pi^2 -100\pi^2$

Correct answer:

$x^2\pi-20x\pi+100\pi$

Explanation:

Write the formula for the area of a circle.

$A= \pi r^2$

Substitute the radius into the formula.

$A= \pi (x-10)^2 = \pi (x-10)(x-10)$

Use the FOIL method to simply the binomials.

$A= \pi [(x)(x)+(-10)(x)+(-10)(x)+(-10)(-10)]$

Simplify and multiply the terms.

$A= \pi [x^2-10x-10x+100]$

Combine like-terms.

$A= \pi [x^2-20x+100]$

Distribute the pi through each term.

$A= \pi [x^2-20x+100] = x^2\pi-20x\pi+100\pi$

The answer is: $A= x^2\pi-20x\pi+100\pi$

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Example Question #63 : Area Of A Circle

Find the area of a circle that has a diameter of 7 inches.

Possible Answers:

$7\pi in^2$

$12.25\pi in^2$

$21\pi in^2$

$49\pi in^2$

$14\pi in^2$

Correct answer:

$12.25\pi in^2$

Explanation:

The formula for finding the area of a circle is $\pi r^2$ .

The radius of the problem is half of the diameter which would be 3.5.

Therefore it would be $3.5^2 * \pi$ .

Which equals $12.25\pi in^2$

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Example Question #64 : Area Of A Circle

A cicle has a circumference of $22\pi$ . What is the area of the circle?

Possible Answers:

Not enough information

$44\pi$

$484\pi$

$22\pi$

$121\pi$

Correct answer:

$121\pi$

Explanation:

The circumference of a circle is equal to:

$C=2\pi r$

Because we know that the circumference is $22\pi$ , we simply set the formula equal to $22\pi$ to find the radius, or :

$22\pi=2\pi r$

$\frac{22\pi}{2\pi}=\frac{2\pi r}{2\pi}$

r=11

Now that we have the radius, we can plug it into the formula for the area of a circle which is:

$A=\pi r^2$

$A=\pi (11)^2$

$A=121\pi$

Therefore, the area of the circle is $121\pi$ .

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Example Question #184 : Area

Find the area of a circle with a diameter of 13cm.

Possible Answers:

$169\pi \ \text{cm}^2$

$13\pi \ \text{cm}^2$

$36\pi \ \text{cm}^2$

$42.25\pi \ \text{cm}^2$

$26\pi \ \text{cm}^2$

Correct answer:

$42.25\pi \ \text{cm}^2$

Explanation:

The formula to find the area of a circle is

$A = \pi r^2$

where r is the radius. Now, we know the diameter is 13cm. We also know the radius is half the diameter, so the radius is 6.5cm. So, we substitute and get

$A = \pi \cdot (6.5 \text{cm})^2$

$A = \pi \cdot 42.25\text{cm}^2$

$A = 42.25\pi \ \text{cm}^2$

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Example Question #65 : Area Of A Circle

Find the area of a circle with radius of 4 meters.

Possible Answers:

$16 \pi m^$

$8 \pi m^2$

$16 \pi m^2$

16 m^2

Correct answer:

$16 \pi m^2$

Explanation:

Find the area of a circle with radius of 4 meters.

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

$A=\pi r^2$

Now, we know our radius is 4 meters, so we need to plug it in and solve for A.

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

Pay close attention to the units. We are dealing with area, which is 2 dimensional, so we need squared units.

$16 \pi m^2$

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Example Question #66 : Area Of A Circle

Find the area of a circle with a diameter of 12cm. $(\pi = 3.14)$

Possible Answers:

$37.68\text{cm}^2$

$18.84\text{cm}^2$

$452.16\text{cm}^2$

$113.04\text{cm}^2$

$39.14\text{cm}^2$

Correct answer:

$113.04\text{cm}^2$

Explanation:

The formula to find the area of a circle is

$A = \pi r^2$

where r is the radius. We know the diameter of the circle is 12cm. We also know the radius is half the diameter, so in this case, the radius is 6cm. The value of $\pi$ is given as 3.14. Knowing this, we can substitute into the equation. We get

$A = 3.14 \cdot (6\text{cm})^2$

$A = 3.14 \cdot 36\text{cm}^2$

$A = 113.04\text{cm}^2$

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Example Question #67 : Area Of A Circle

Mike and Joe are playing frisbee. Their frisbee has a diameter of inches.

What is the area of the frisbee?

Possible Answers:

$4\pi in ^2$

$8\pi in^2$

$16\pi in ^2$

$64 \pi in^2$

$24\pi in^2$

Correct answer:

$16\pi in ^2$

Explanation:

The formula for the area of a circle is $\pi r^2$ .

The radius of the frisbee is 4 inches.

$\pi * 4^2$

$= 16\pi in^2$

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Pre-Algebra : Area of a Circle

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #61 : Area Of A Circle

Example Question #172 : Area

Example Question #173 : Area

Example Question #62 : Area Of A Circle

Example Question #63 : Area Of A Circle

Example Question #64 : Area Of A Circle

Example Question #184 : Area

Example Question #65 : Area Of A Circle

Example Question #66 : Area Of A Circle

Example Question #67 : Area Of A Circle

All Pre-Algebra Resources

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