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High School Math : How to find the area of a circle

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Example Questions

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

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

Possible Answers:

$16\pi$

$64\pi$

$32\pi$

$8\pi$

Correct answer:

$64\pi$

Explanation:

To find the area of a circle you must plug the radius into in the following equation.

In this case, the radius is , so we plug into .

$A=\pi(8)^2=\pi(64)$

$A=64\pi$

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

What is the area of a circle with a radius of 9?

Possible Answers:

$81\pi$

$18\pi$

$24\pi$

$9\pi$

Correct answer:

$81\pi$

Explanation:

To find the area of a circle you must plug the radius into in the following equation

In this case the radius is 9 so we plug it into to get $9^{2}=81$

We then multiply it by $\pi$ to get our answer $A=81\pi$

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Example Question #2 : How To Find The Area Of A Circle

Circle_with_radius

Find the area of a circle with a radius of r=6m .

Possible Answers:

$36\pi m^{2}$

Not enough information to solve

$\dpi{100} 6\pi m^{2}$

$\dpi{100} 63\pi m^{2}$

$36m^{2}$

Correct answer:

$36\pi m^{2}$

Explanation:

In order to find the circle's area, utilize the formula $\dpi{100} A=\pi r^{2}$ .

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

$\dpi{100} A=\pi (6m)^{2}$

$\dpi{100} \rightarrow 36\pi m^{2}$

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Example Question #3 : How To Find The Area Of A Circle

Circle_with_radius

A circle has a radius r=5in , what is its area?

Possible Answers:

$\dpi{100} 5\pi in^{2}$

$\dpi{100} 25 in^{2}$

Not enough information to solve

$\dpi{100} 25\pi^{2} in^{2}$

$25\pi in^{2}$

Correct answer:

$25\pi in^{2}$

Explanation:

In order to find the circle's area, utilize the formula $\dpi{100} A=\pi r^{2}$ .

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

$A=\pi (5in)^{2}$

$\rightarrow 25\pi in^{2}$

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Example Question #3 : Radius

Circle_with_diameter

A circle has a diameter $D=\pi$ , what is its area?

Possible Answers:

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

$\frac{\pi^{3}}{4}$

$\dpi{100} \frac{\pi^{2}}{4}$

$\pi^{3}$

Not enough information to solve

Correct answer:

$\frac{\pi^{3}}{4}$

Explanation:

In order to find the circle's area, utilize the formula $\dpi{100} A=\pi r^{2}$ .

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

However, we need to convert our diameter into a radius.

D=2r

$\pi=2r$

Solve for .

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

Insert the radius into the area formula and solve.

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

$A=\pi*\frac{\pi^{2}}{4}$

$A=\frac{\pi}{1}*\frac{\pi^{2}}{4}$

$\rightarrow \frac{\pi^{3}}{4}$

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Example Question #4 : How To Find The Area Of A Circle

Circles

Refer to the above drawing. This shows a ring-shaped garden with inner radius 20 feet and outer radius 40 feet. To the nearest square foot, what is the area of the garden?

Possible Answers:

$1,885 \; \textrm{ft}^{2}$

$3,770 \; \textrm{ft}^{2}$

$2,514 \; \textrm{ft}^{2}$

$2,827 \; \textrm{ft}^{2}$

$1,257 \; \textrm{ft}^{2}$

Correct answer:

$3,770 \; \textrm{ft}^{2}$

Explanation:

The total area of the garden is the area of the outer circle - R = 40 - minus that of the inner circle - r=20 .

$A = \pi R^{2} - \pi r^{2} = \pi \cdot 40^{2} - \pi \cdot 20^{2} \approx 5,027 - 1,257 =3,770$

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Example Question #5 : How To Find The Area Of A Circle

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

Possible Answers:

$25\pi$

$5\pi$

$10\pi$

Correct answer:

$25\pi$

Explanation:

To find the area of a circle you must plug the radius into the following equation

In this case the radius is so we plug it in and square it to get $5^{2}=25$

We then multiply it by $\pi$ to get our answer $A=25\pi$

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Example Question #7 : Radius

Four circles are drawn inside of a square. What is the area of the shaded region?

Possible Answers:

$32\pi$

$4\pi$

$8\pi$

$16\pi$

Correct answer:

$16\pi$

Explanation:

Each set of two circles fits perfectly between the sides of the square. The diameters of two of the circle must equal the length of one side of the square.

2d=s

Each side has a length of 8 and the diameter of a circle is twice the radius. We can use these relationships to substitute into the first equation.

$d=2r\ \text{and}\ s=8$

2(2r)=8

Solve for the radius, $\small r$ .

$r=(8)(\frac{1}{4})=2$

The area of a circle can be calculated using the equation $A=r^2\pi$ . The shaded region is made of four circles, all with the same radius.

The area of one circle is given below.

$A=r^2\pi=2^2\pi=4\pi$

The area of the shaded region (four circles) would be $4(4\pi)=16\pi$ .

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Example Question #1 : Radius

O, M, and I represent three circles. Each circle shares the same center point. What is the area of the shaded region?

Possible Answers:

$17\pi$

$64\pi$

$26\pi$

$54\pi$

Correct answer:

$54\pi$

Explanation:

The area of the shaded region can be found by using the areas of the individual circles. The area of the full figure is the area of circle O. The area of the center shaded area is the area of circle I. Circle M contains circle I. The area of the shaded region will be equal to A_O-A_M+A_I .

First, find the area of each circle using $\small A_{circ}=\pi r^2$ .

$r_O=3+3+\frac{1}{2}6=9$

$A_O=\pi (9)^2=81\pi$

$r_M=3+\frac{1}{2}6=6$

$A_M=\pi(6)^2=36\pi$

$r_I=\frac{1}{2}6=3$

$A_I=\pi(3)^2=9\pi$

Now we can substitute into our equation.

A_O-A_M+A_I

$81\pi-36\pi+9\pi$

$54\pi$

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Example Question #7 : How To Find The Area Of A Circle

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

Possible Answers:

$5\pi$

$10\pi$

$2.5\pi$

$100\pi$

$25\pi$

Correct answer:

$25\pi$

Explanation:

The formula for area of a circle is $A=\pi r^2$ . Unfortunately, the problem gives us a diameter instead of a radius. The good news is that the diameter is equal to twice the length of the radius or, mathematically, d=2r .

Plug in the given diameter to find the radius:

d=2r

10=2r

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

5=r

Plug that into our first equation to solve:

$A=\pi r ^2$

$A=\pi 5^2$

$A=25\pi$

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High School Math : How to find the area of a circle

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

Example Question #2 : How To Find The Area Of A Circle

Example Question #3 : How To Find The Area Of A Circle

Example Question #3 : Radius

Example Question #4 : How To Find The Area Of A Circle

Example Question #5 : How To Find The Area Of A Circle

Example Question #7 : Radius

Example Question #1 : Radius

Example Question #7 : How To Find The Area Of A Circle

All High School Math Resources

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