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ACT Math : How to find the area of a circle

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Example Question #561 : Act Math

What is the area of a cirlce with a circumference of $24\pro\pi$ ?

Possible Answers:

$144\pi$

$48\pi$

$24\pi$

$576\pi$

$36\pi$

Correct answer:

$144\pi$

Explanation:

The formula for the circumference of a circle is $c = 2*\pi*r$ . Because we are given the circumference we substitute $24\pi$ for and solve for , yielding r = 12 .

Next, we need to plug in our value for into the formula for the area of a circle.

$A = \pi * r^{2}$ and get

$A = 144\pi$

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Example Question #32 : Radius

A circle has a cricumference of $16\pi$ . Given this information, find the area of the circle.

Possible Answers:

$64\pi$

$8\pi$

$64\pi^2$

$16\pi$

Correct answer:

$64\pi$

Explanation:

To find the area of a circle, we use the formula

$A=\pi r^2$

where r is the radius.

However, the problem does not give us the circles radius. In order to solve for the area we must find the radius using the circumference. Circumference of a circle follows the equation

$C=2\pi r$ ,

so since we know the circumference we can manipulate the equation and plug in our value to solve for radius.

$r=\frac{C}{2\pi}=\frac{16\pi}{2\pi}=8$ .

Now that we know the radius we simply plug it into the area formula to solve for our final answer.

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

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Example Question #41 : How To Find The Area Of A Circle

In the following diagram, the radius is given. What is area of the shaded region?

Circle_box

Possible Answers:

$64 x^{2} - 16\pi x^{2}$

$32 x^{2} -8\pi x^{2}$

$64 x^{2} -8\pi x^{2}$

$32 x^{2} - 16\pi x^{2}$

$16x^{2}$

Correct answer:

$32 x^{2} -8\pi x^{2}$

Explanation:

This question asks you to apply the concept of area in finding both the area of a circle and square. Since the cirlce is inscribed in the square, we know that its diameter (two times the radius) is the same length as one side of the square. Since we are given the radius, , we can find the area of both the circle and square.

Square:

This gives us the area for the entire square.

The bottom half of the square has area $\frac{1}{2} \cdot 64x^{}2 = 32x^{}2$ .

Now that we have this value, we must find the area that the circle occupies. The area of a circle is given by $\pi \cdot r^{}2$ .

So the area of this circle will be $\pi \cdot 16x^{}2$ .

The bottom half of the circle has half that area:

$\rightarrow \pi \cdot 8x^{}2$

Now that we have both our values, we can subtract the bottom half of the circle from the bottom half of the square to give us the shaded region:

$32 x^{}2 - \pi \cdot 8x^{}2$

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Example Question #31 : How To Find The Area Of A Circle

What is the area of a circle, in terms of $\pi$ , that has a radius of 6 inches?

Possible Answers:

$144\pi in^2$

$36\pi in^2$

$12 \pi in^2$

$10 \pi in^2$

$9\pi in^2$

Correct answer:

$36\pi in^2$

Explanation:

To find the area of a circle with a given radius, use the formula:

$\\A = \pi r^2 \\A= \pi 6^2 \\A= 36\pi in^2$

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Example Question #32 : How To Find The Area Of A Circle

Find the area of a circle given the radius is 8.

Possible Answers:

$16\pi$

$64\pi$

$8\pi$

$128\pi$

Correct answer:

$64\pi$

Explanation:

To solve, simply use the formula for area of a circle.

Since the question gives us the value of the radius, we can substitute 8 in for the radius to solve for the area.

Thus,

$A=\pi{r^2}=\pi*8^2=64\pi$

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Example Question #101 : Circles

Find the area of a circle given a radius of 1.

Possible Answers:

$2\pi$

$0.5\pi$

$4\pi$

$\pi$

Correct answer:

$\pi$

Explanation:

To solve, simply use the formula for the area of a circle.

In this particular case, substitute one in for the radius in the following equation.

Thus,

$A=\pi{r^2}=\pi*1^2=\pi*1=\pi$

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Example Question #574 : Plane Geometry

A circle has a maximum chord length of inches. What is its area in square inches?

Possible Answers:

$81\pi$

$64\pi$

$36\pi$

$49\pi$

$25\pi$

Correct answer:

$49\pi$

Explanation:

We can use the fact that the longest chord of a circle is its diameter.

In other words, this circle has a diameter of inches, meaning a radius of inches.

$\\d=2r\\ 14=2r\\ 7=r$

From there, finding the area is straightforward:

$A = \pi r^2 = \pi*7^2 = 49\pi$

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

If a circle has circumference $8\pi$ , what is its area?

Possible Answers:

$16\pi$

$4\pi$

$8\pi$

Correct answer:

$16\pi$

Explanation:

If the circumference is $8\pi$ , then since $C=2\pi r$ we know r=4 . We further know that $A=\pi r2$ , so $A=\pi (4)^2=16\pi.$

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ACT Math : How to find the area of a circle

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #561 : Act Math

Example Question #32 : Radius

Example Question #41 : How To Find The Area Of A Circle

Example Question #31 : How To Find The Area Of A Circle

Example Question #32 : How To Find The Area Of A Circle

Example Question #101 : Circles

Example Question #574 : Plane Geometry

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

All ACT Math Resources

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