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Common Core: 7th Grade Math : Area of a circle

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

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Example Questions

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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Example Question #14 : Area Of A Circle

What is the area of the circle provided?

Possible Answers:

$53\pi\textup{ in}^2$

$50\pi\textup{ in}^2$

$49\pi\textup{ in}^2$

$52\pi\textup{ in}^2$

$51\pi\textup{ in}^2$

Correct answer:

$49\pi\textup{ in}^2$

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:

$A=7^2\pi$

Solve:

$A=49\pi\textup{ in}^2$

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Example Question #15 : Area Of A Circle

What is the area of the circle provided?

Possible Answers:

$121\pi\textup{ in}^2$

$122\pi\textup{ in}^2$

$123\pi\textup{ in}^2$

$124\pi\textup{ in}^2$

$120\pi\textup{ in}^2$

Correct answer:

$121\pi\textup{ in}^2$

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:

$A=11^2\pi$

Solve:

$A=121\pi\textup{ in}^2$

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Example Question #16 : Area Of A Circle

What is the area of the circle provided?

Possible Answers:

$223\pi\textup{ in}^2$

$224\pi\textup{ in}^2$

$222\pi\textup{ in}^2$

$225\pi\textup{ in}^2$

$226\pi\textup{ in}^2$

Correct answer:

$225\pi\textup{ in}^2$

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:

$A=15^2\pi$

Solve:

$A=225\pi\textup{ in}^2$

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Example Question #17 : Area Of A Circle

What is the area of the circle provided?

Possible Answers:

$442\pi\textup{ in}^2$

$440\pi\textup{ in}^2$

$444\pi\textup{ in}^2$

$441\pi\textup{ in}^2$

$443\pi\textup{ in}^2$

Correct answer:

$441\pi\textup{ in}^2$

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:

$A=21^2\pi$

Solve:

$A=441\pi\textup{ in}^2$

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Example Question #14 : Area Of A Circle

What is the area of the circle provided?

Possible Answers:

$1\textup,026\pi\textup{ in}^2$

$1\textup,023\pi\textup{ in}^2$

$1\textup,022\pi\textup{ in}^2$

$1\textup,024\pi\textup{ in}^2$

$1\textup,025\pi\textup{ in}^2$

Correct answer:

$1\textup,024\pi\textup{ in}^2$

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:

$A=32^2\pi$

Solve:

$A=1\textup,024\pi\textup{ in}^2$

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Common Core: 7th Grade Math : Area of a circle

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

All Common Core: 7th Grade Math Resources

Example Questions

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

Example Question #14 : Area Of A Circle

Example Question #15 : Area Of A Circle

Example Question #16 : Area Of A Circle

Example Question #17 : Area Of A Circle

Example Question #14 : Area Of A Circle

All Common Core: 7th Grade Math Resources

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