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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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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Example Question #191 : High School Math

This figure is a circle with a radius of 3 cm. Circle

What is the area of the circle (cm²)?

Possible Answers:

$15\pi$

$36\pi$

$12\pi$

$9\pi$

$6\pi$

Correct answer:

$9\pi$

Explanation:

The area of the circle is $\pi\cdo$ times radius squared ( $\pi\cdot3^{2}$ ).

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Example Question #192 : High School Math

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

Possible Answers:

$8\pi$

$16\pi$

$4\pi$

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

If the equation of a circle is (x – 7)²+ (y + 1)²= 81, what is the area of the circle?

Possible Answers:

18π

81π

49π

2π

6561π

Correct answer:

81π

Explanation:

The equation is already in a circle equation, and the right side of the equation stands for r^2 →r²= 81 and r = 9

The area of a circle is πr², so the area of this circle is 81π.

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

Assume π = 3.14

A man would like to put a circular whirlpool in his backyard. He would like the whirlpool to be six feet wide. His backyard is 8 feet long by 7 feet wide. By state regulation, in order to put a whirlpool in a backyard space, the space must be 1.5 times bigger than the pool. Can the man legally install the whirlpool?

Possible Answers:

Yes, because the area of the whirlpool is 18.84 square feet and 1.5 times its area would be less than the area of the backyard.

No, because the area of the whirlpool is 42.39 square feet and 1.5 times its area would be greater than the area of the backyard.

Yes, because the area of the whirlpool is 28.26 square feet and 1.5 times its area would be less than the area of the backyard.

No, because the area of the backyard is smaller than the area of the whirlpool.

No, because the area of the backyard is 30 square feet and therefore the whirlpool is too big to meet the legal requirement.

Correct answer:

Yes, because the area of the whirlpool is 28.26 square feet and 1.5 times its area would be less than the area of the backyard.

Explanation:

If you answered that the whirlpool’s area is 18.84 feet and therefore fits, you are incorrect because 18.84 is the circumference of the whirlpool, not the area.

If you answered that the area of the whirlpool is 56.52 feet, you multiplied the area of the whirlpool by 1.5 and assumed that that was the correct area, not the legal limit.

If you answered that the area of the backyard was smaller than the area of the whirlpool, you did not calculate area correctly.

And if you thought the area of the backyard was 30 feet, you found the perimeter of the backyard, not the area.

The correct answer is that the area of the whirlpool is 28.26 feet and, when multiplied by 1.5 = 42.39, which is smaller than the area of the backyard, which is 56 square feet.

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #191 : High School Math

Example Question #192 : High School Math

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

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

All High School Math Resources

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