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

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Example Question #1 : Area Of A Circle

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

Possible Answers:

$4$

$2$

$4\pi$

$2\pi$

$\pi$

Correct answer:

$4$

Explanation:

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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Example Question #81 : Circles

What is the area of a circle whose diameter is 8?

Possible Answers:

16π

8π

12π

32π

64π

Correct answer:

16π

Explanation:

Circarea

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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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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 : Area Of A Circle

Example Question #81 : Circles

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

All High School Math Resources

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