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Common Core: 7th Grade Math : Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

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Example Questions

Example Question #1 : Area Of A Circle

The circumference of a circle is 12.56 inches. Find the area of the circle.

Let $\pi = 3.14$ .

Possible Answers:

$11\ in^2$

$12\ in^2$

$13.56\ in^2$

$12.56\ in^2$

$11.56\ in^2$

Correct answer:

$12.56\ in^2$

Explanation:

First we need to find the radius of the circle. The circumference of a circle is $Circumference =2\pi r$ , where is the radius of the circle.

$12.56=2\times 3.14\times r\Rightarrow r=2\ in$

The area of a circle is $Area=\pi r^2$ where is the radius of the circle.

$Area=\pi r^2=3.14\times 2^2=12.56\ in^2$

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Example Question #1 : Radius

The radius of a circle is 4 cm, what is the area?

Possible Answers:

$50.2\ cm^{2}$

$78\ cm^{2}$

$12.6\ cm^{2}$

$28.3\ cm^{2}$

$58.7\ cm^{2}$

Correct answer:

$50.2\ cm^{2}$

Explanation:

The area of a circle is found by: $Area=r^{2}\pi$ , where r is the radius.

$4^{2} \pi = 50.2$ .

The area of the circle is $50.2\ cm^{2}$ .

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Example Question #1 : Radius

The radius, , of the circle below is 18 units. What is the area of the circle?

Circle

Possible Answers:

$36\pi$ square units

$18\pi$ square units

Cannot be determined

$324\pi$ square units

324 square units

Correct answer:

$324\pi$ square units

Explanation:

The formula for the area, , of a circle with radius is:

$A=\pi R^{2}$

We can fill in

$A=\pi (18^{2})$

$A=324\pi$

You could do the arithmetic to get an area of about 1,017.876 square units, but it is ok and more precise to leave it as shown.

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Example Question #1 : How To Find The Area Of A Circle

Give the area of a circle with diameter 13.

Possible Answers:

$13 \pi$

$\frac{169\pi }{4}$

$26 \pi$

$\frac{169\pi }{2}$

$\frac{13\pi }{2}$

Correct answer:

$\frac{169\pi }{4}$

Explanation:

Half of the diameter 13 is the radius $\frac{13}{2}$ . Use the area formula:

$A = \pi r^{2} = \pi \cdot \left ( \frac{13}{2} \right )^{2} = \frac{169\pi }{4}$

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Example Question #402 : Geometry

How many times greater is the area of a circle with a radius of 4in., compared to a circle with a radius of 2in.?

Possible Answers:

$4$

$2\pi$

$\pi$

$2$

$4\pi$

Correct answer:

$4$

Explanation:

The area of a circle can be solved using the equation $A=\pi r^{2}$

The area of a circle with radius 4 is $\pi 4^{2}=16\pi$ while the area of a circle with radius 2 is $\pi 2^{2}=4\pi$ . $16\pi \div 4\pi =4$

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Example Question #11 : Area Of A Circle

Find the area of a circle that has a radius of $\frac{1}{5}$ .

Possible Answers:

$\frac{1}{10}\pi$

$\frac{1}{25}\pi$

$\frac{1}{5}$

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

Correct answer:

$\frac{1}{25}\pi$

Explanation:

Use the following formula to find the area of a circle:

$\text{Area}=\pi \times \text{radius}^2$

For the circle in question, plug in the given radius to find the area.

In our particular case the radius is $\frac{1}{5}$ .

$\text{Area}=\pi \times \left(\frac{1}{5}\right)^2=\frac{1}{25}\pi$

When squarring a fraction we need to square both the numerator and the denominator.

$\pi \times \left(\frac{1}{5}\right)^2=\frac{1^2}{5^2}\pi=\frac{1\cdot 1}{5\cdot 5}\pi=\frac{1}{25}\pi$

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Example Question #12 : Area Of A Circle

Find the area of a circle that has a radius of $\sqrt5$ .

Possible Answers:

$\sqrt{10}\pi$

$\sqrt{5}\pi$

$2\sqrt5 \pi$

$5\pi$

Correct answer:

$5\pi$

Explanation:

Use the following formula to find the area of a circle:

$\text{Area}=\pi \times \text{radius}^2$

For the circle in question, plug in the given radius to find the area.

In this problem the known radius is $\sqrt5$

Now plug the radius into the area equation.

$\text{Area}=\pi \times \text{radius}^2$

Therefore we get,

$\text{Area}=\pi \times (\sqrt5)^2=5\pi$

Recall that when a square root is squared you are left with the number under the square root sign. This happens because when you square a number you are multiplying it by itself. In our case this is,

$(\sqrt{5})^2=\sqrt{5}\cdot \sqrt{5}$ .

From here we can use the property of multiplication and radicals to rewrite our expression as follows,

$\sqrt{5}\cdot \sqrt{5}=\sqrt{5\cdot 5}$

and when there are two numbers that are the same under a square root sign you bring out one and the other number and square root sign go away.

$\sqrt{5\cdot 5}=5$

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Example Question #11 : How To Find The Area Of A Circle

What is the area of a circle with a diameter of , rounded to the nearest whole number?

Possible Answers:

$\dpi{100} 81$

$\dpi{100} 64$

$\dpi{100} 255$

$\dpi{100} 254$

Correct answer:

$\dpi{100} 64$

Explanation:

The formula for the area of a circle is

$\dpi{100} \pi r^{2}$

Find the radius by dividing 9 by 2:

$\dpi{100} \frac{9}{2}=4.5$

So the formula for area would now be:

$\dpi{100} \pi r^{2}=\pi (4.5)^{2}=20.25\pi \approx 63.6= 64$

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Example Question #13 : Area Of A Circle

If this circle has a diameter of 12 inches, what is its area?

Circle_12d

Possible Answers:

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

None of the other answers are correct.

$116\ \text{inches}^{2}$

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

$48\pi\ \text{inches}^{2}$

Correct answer:

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

Explanation:

To find the area, we need to determine the radius of the circle first.

The radius is calculated as $r=\frac{D}{2}$ , where D is the diameter.

Given that the diameter is 12 inches, the radius is $r=\frac{12}{2}$ , or $r=6\ \text{inches}$ .

Next, we know that the formula for the area of the circle is $A=\pi r^2$ .

Using the radius we just found, we can find the area:

$A=\pi (6)^2=36\pi\ \text{inches}$

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Example Question #13 : Area Of A Circle

What is the area of the circle provided?

Possible Answers:

$6\pi\textup{ in}^2$

$9\pi\textup{ in}^2$

$8\pi\textup{ in}^2$

$7\pi\textup{ in}^2$

$5\pi\textup{ in}^2$

Correct answer:

$9\pi\textup{ in}^2$

Explanation:

In order to solve this problem, we need to recall the formula for the area of a circle:

$A= r^2\pi$

The circle in this question provides us with the radius, so we can use the formula to solve:

$A=3^2\pi$

Solve:

$A=9\pi\textup{ in}^2$

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Common Core: 7th Grade Math : Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #1 : Area Of A Circle

Example Question #1 : Radius

Example Question #1 : Radius

Example Question #1 : How To Find The Area Of A Circle

Example Question #402 : Geometry

Example Question #11 : Area Of A Circle

Example Question #12 : Area Of A Circle

Example Question #11 : How To Find The Area Of A Circle

Example Question #13 : Area Of A Circle

Example Question #13 : Area Of A Circle

All Common Core: 7th Grade Math Resources

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