Area of a Circle - Pre-Algebra

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Question

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

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Answer

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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Question

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

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Answer

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.

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

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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Question

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

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Answer

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 :

$22\pi=2\pi r$

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

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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Question

What is the area of a circle with a radius of ?

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Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius and solve for area.

$A=\pi (15)^2 = 225\pi$

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Question

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

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Answer

If the diameter is 7, then the radius is half of 7, or 3.5.

Plug this value for the radius into the equation for the area of a circle:

$A=r^2\pi=(3.5)^2\pi=12.25\pi$

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Question

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

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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

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

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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?

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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.

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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 .

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

Let $\pi = 3.14$ .

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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

A circle has a circumference of $\small 6\pi$ . What is its area?

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Answer

To begin, we need to find the radius of the circle. The circumference of a circle is given as follows:

$\small C = 2\pi r$ ,

where is the radius.

Then, a circle with circumference $6\pi$ will have the following radius:

$6\pi = 2\pi r$

$\small \frac{6\pi}{2\pi}=\frac{2\pi r}{2\pi}$

$\small 3=r$

Using the radius, we can now solve for the area:

$\small A=\pi r^2$

$A=\pi(3)^2$

$\small A=9\pi$

The area of the circle is $\small 9\pi$ .

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Question

A circle has a diameter of inches. What is the area of the circle? Round to the nearest tenth decimal place.

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Answer

The formula to find the area of a circle is $A=\pi\cdot r^2$ .

First you must find the radius from the diameter.

$r=\frac{1}{2}d \rightarrow r=\frac{1}{2}\cdot 10=5$

In this case it is,

$A=5^2 \cdot \pi = 25\cdot 3.14= 78.5$

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Question

The rectangle in the above figure has length 20 and height 10. What is the area of the orange region?

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Answer

The orange region is a composite of two figures:

One is a rectangle measuring 20 by 10, which, subsequently, has area

$20 \cdot 10 = 200$ .

The other is a semicircle with diameter 10, and, subsequently, radius 5. Its area is

$\frac{1}{2} \pi \cdot 5^{2} = \frac{25}{2} \pi$ .

Add the areas:

$A = 200 + \frac{25}{2} \pi$

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Question

Units = cm

Radius is five, find the area of the circle.

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Answer

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is five. To solve for the area, we just plug it into our equation:

$\ A=\small \small \small \pi(5)^{2} \ A= 5\times5 \times \pi \A= 25\pi \A= 25 \times 3.14 \A= 78.5cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small 78.5cm^{2}$ .

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Question

Units = cm

Radius is $\small 6.5$ , find the area of the circle.

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Answer

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is 6.5.

To solve for the area, we just plug it into our equation:

$\A=\small \small \small \small \pi(6.5)^{2} \A= 6.5\times6.5 \times \pi \A= 42.45\pi \A= 42.25 \times 3.14\A = 132.665cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small 132.665cm^{2}$ .

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Question

Units = cm

Radius is four, find the area of the circle.

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Answer

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is four. To solve for the area, we just plug it into our equation:

$\A=\small \small \small \small \small \pi(4)^{2}\A = 4\times4 \times \pi \A=16\pi \A= 16 \times 3.14 \A= 50.24cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small 50.24cm^{2}$ .

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Question

Units = cm

Radius is two, find the area of the circle.

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Answer

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is two.

To solve for the area, we just plug it into our equation:

$\ A=\small \small \small \small \small \small \pi(2)^{2} \A= 2\times2\times \pi \A=4\pi \A=4 \times 3.14 \A= 12.56cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small \small 12.56cm^{2}$ .

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Question

Units = cm

Radius is ten, find the area of the circle.

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Answer

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is ten.

To solve for the area, we just plug it into our equation:

$\A=\small \small \small \small \small \small \small \pi(10)^{2} \A= 10\times10\times \pi \A=100\pi \A=4 \times 3.14 \A= 314cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small \small \small 314cm^{2}$ .

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Question

Units = cm

Diameter is 16, find the area of the circle.

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Answer

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the diameter of the circle, meaning the radius is half of this. To solve for the area, we just plug it into our equation:

$r=\frac{1}{2}d\rightarrow r=\frac{1}{2}16=8$

$\A=\small \small \small \small \pi(8)^{2} = 8\times8\times \pi \A= 64\pi \A= 64 \times 3.14 \A= 200.96cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small200.96cm^{2}$ .

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