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High School Math : 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 #45 : Radius

Find the area of a circle with a circumference of $16\pi m$ .

Possible Answers:

$48\pi m^2$

$64\pi m^2$

$32\pi m^2$

$52\pi m^2$

$16\pi m^2$

Correct answer:

$64\pi m^2$

Explanation:

The formula for the circumference of a circle is:

$C=2\pi r$ ,

where is the radius of the circle.

To solve for the radius, plug in our existing values:

$16\pi m=2\pi r$

r=8m

The formula for the area of a circle is:

$A=\pi (r)^2$ ,

where is the radius of the circle.

Plugging in our values, we get:

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

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Example Question #46 : Radius

Find the area of the following circle:

Possible Answers:

$39 \pi\ m^2$

$29 \pi\ m^2$

$59 \pi\ m^2$

$69 \pi\ m^2$

$49 \pi\ m^2$

Correct answer:

$49 \pi\ m^2$

Explanation:

The formula for the area of a circle is

$A = \pi (r)^2$ ,

where is the radius of the circle.

Plugging in our values, we get:

$A = \pi (7\ m)^2$

$A = 49 \pi\ m^2$

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Example Question #101 : Plane Geometry

Two equal circles are cut out of a rectangular sheet of paper with the dimensions 10 by 20. The circles were made to have the greatest possible diameter. What is the approximate area of the paper after the two circles have been cut out?

Figure_2

Possible Answers:

Correct answer:

Explanation:

The length of 20 represents the diameters of both circles. Each circle has a diameter of 10 and since radius is half of the diameter, each circle has a radius of 5. The area of a circle is A = πr² . The area of one circle is 25π. The area of both circles is 50π. The area of the rectangle is (10)(20) = 200. 200 - 50π gives you the area of the paper after the two circles have been cut out. π is about 3.14, so 200 – 50(3.14) = 43.

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Example Question #102 : Plane Geometry

Screen_shot_2013-03-18_at_10.29.01_pm

Kate has a ring-shaped lawn which has an inner radius of 10 feet and an outer radius 25 feet. What is the area of her lawn?

Possible Answers:

525π ft²

325π ft²

275π ft²

175π ft²

125π ft²

Correct answer:

525π ft²

Explanation:

The area of an annulus is

$\pi (R^{2}-r^{2})$

where is the radius of the larger circle, and is the radius of the smaller circle.

$\pi (25^{2}-10^{2})$

$\pi (625-100)$

$525\pi$

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Example Question #103 : Plane Geometry

A 6 by 8 rectangle is inscribed in a circle. What is the area of the circle?

Possible Answers:

$10\pi$

$4\pi$

$25\pi$

$20\pi$

Correct answer:

$25\pi$

Explanation:

The image below shows the rectangle inscribed in the circle. Dividing the rectangle into two triangles allows us to find the diameter of the circle, which is equal to the length of the line we drew. Using a²+b²= c² we get 6²+ 8² = c². c² = 100, so c = 10. The area of a circle is $A=\pi r^2$ . Radius is half of the diameter of the circle (which we know is 10), so r = 5.

$A=\pi *5^2=25\pi$

Diagram_1

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Example Question #234 : High School Math

A park wants to build a circular fountain with a walkway around it. The fountain will have a radius of 40 feet, and the walkway is to be 4 feet wide. If the walkway is to be poured at a depth of 1.5 feet, how many cubic feet of concrete must be mixed to make the walkway?

Possible Answers:

None of the other answers are correct.

$504\pi \ ft^{3}$

$1296\pi \ ft^{3}$

$1936\pi \ ft^{3}$

$336\pi \ ft^{3}$

Correct answer:

$504\pi \ ft^{3}$

Explanation:

The following diagram will help to explain the solution:

Foutain

We are searching for the surface area of the shaded region. We can multiply this by the depth (1.5 feet) to find the total volume of this area.

The radius of the outer circle is 44 feet. Therefore its area is 44²π = 1936π. The area of the inner circle is 40²π = 1600π. Therefore the area of the shaded area is 1936π – 1600π = 336π. The volume is 1.5 times this, or 504π.

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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:

$2\pi$

$4\pi$

$\pi$

$2$

$4$

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 #231 : High School Math

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

Possible Answers:

8π

32π

16π

12π

64π

Correct answer:

16π

Explanation:

Circarea

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Example Question #31 : 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:

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

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

$16x^{2}$

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

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

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 #232 : High School Math

In a large field, a circle with an area of 144π square meters is drawn out. Starting at the center of the circle, a groundskeeper mows in a straight line to the circle's edge. He then turns and mows ¼ of the way around the circle before turning again and mowing another straight line back to the center. What is the length, in meters, of the path the groundskeeper mowed?

Possible Answers:

24 + 36π

24 + 6π

12 + 36π

24π

12 + 6π

Correct answer:

24 + 6π

Explanation:

Circles have an area of πr², where r is the radius. If this circle has an area of 144π, then you can solve for the radius:

πr² = 144π

r ² = 144

r =12

When the groundskeeper goes from the center of the circle to the edge, he's creating a radius, which is 12 meters.

When he travels ¼ of the way around the circle, he's traveling ¼ of the circle's circumference. A circumference is 2πr. For this circle, that's 24π meters. One-fourth of that is 6π meters.

Finally, when he goes back to the center, he's creating another radius, which is 12 meters.

In all, that's 12 meters + 6π meters + 12 meters, for a total of 24 + 6π meters.

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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 #45 : Radius

Example Question #46 : Radius

Example Question #101 : Plane Geometry

Example Question #102 : Plane Geometry

Example Question #103 : Plane Geometry

Example Question #234 : High School Math

Example Question #1 : Area Of A Circle

Example Question #231 : High School Math

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

Example Question #232 : High School Math

All High School Math Resources

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