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

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

Give the area of a circle with diameter 13.

Answer

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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Question

What is the area of a circle that has a diameter of inches?

Answer

The formula for finding the area of a circle is $\pi r^{2}$ . In this formula, represents the radius of the circle. Since the question only gives us the measurement of the diameter of the circle, we must calculate the radius. In order to do this, we divide the diameter by .

$\frac{15}{2}=7.5$

Now we use for in our equation.

$\pi (7.5)^{2}=176.7146 : in^{2}$

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Question

What is the area of a circle with a diameter equal to 6?

Answer

First, solve for radius:

$r=\frac{d}{2}=\frac{6}{2}=3$

Then, solve for area:

$A=r^2\pi=3^2\pi=9\pi$

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Question

The diameter of a circle is $4\ cm$ . Give the area of the circle.

Answer

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle, and $\pi$ is approximately .

$Area=\frac{\pi d^2}{4}=\frac{\pi\times 4^2}{4}=4\pi \Rightarrow Area\approx 4\times 3.14\Rightarrow Area\approx 12.56 \ cm^2$

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Question

The diameter of a circle is . Give the area of the circle in terms of .

Answer

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle and $\pi$ is approximately .

$Area=\frac{\pi (4t)^2}{4}=\frac{16\pi t^2}{4}=4\pi t^2 \Rightarrow Area\approx 4\times 3.14\times t^2$

$\Rightarrow Area\approx 12.56t^2$

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Question

The radius of a circle is $\frac{2}{\sqrt{\pi }}$ . Give the area of the circle.

Answer

The area of a circle can be calculated as $Area=\pi r^2$ , where is the radius of the circle, and $\pi$ is approximately .

$Area=\pi r^2=\pi\times (\frac{2}{\sqrt{\pi}})^2=\pi\times \frac{4}{\pi}\Rightarrow Area=4$

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Question

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

Let $\pi = 3.14$ .

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

What is the area of the circle provided?

Answer

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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Question

What is the area of the circle provided?

Answer

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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Question

What is the area of the circle provided?

Answer

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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Question

What is the area of the circle provided?

Answer

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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Question

What is the area of the circle provided?

Answer

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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Question

What is the area of the circle provided?

Answer

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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