How to find the length of a radius

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ACT Math › How to find the length of a radius

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1

A circle has an area of 36π inches. What is the radius of the circle, in inches?

6

CORRECT

18

0

9

0

36

0

Explanation

We know that the formula for the area of a circle is π_r_2. Therefore, we must set 36π equal to this formula to solve for the radius of the circle.

36π = π_r_2

36 = _r_2

6 = r

2

Circle X is divided into 3 sections: A, B, and C. The 3 sections are equal in area. If the area of section C is 12π, what is the radius of the circle?

Act_math_170_02

Circle X

4

0

6

CORRECT

√12

0

7

0

Explanation

Find the total area of the circle, then use the area formula to find the radius.

Area of section A = section B = section C

Area of circle X = A + B + C = 12π+ 12π + 12π = 36π

Area of circle = where r is the radius of the circle

36π = πr2

36 = r2

√36 = r

6 = r

3

A circle has a circumference of . What is the radius of the circle, in feet?

CORRECT

0

0

0

0

Explanation

To answer this question we need to find the radius of the circle given the circumference of .

The equation for a circle's circumference is:

We can plug our circumference into this equation to find the diameter.

We can now divide both sides by

So our diameter is . To find the radius from the diameter, we use the following equation:

So, for this data:

Therefore, the radius of our circle is .

4

A circle has an area of . What is the radius of the circle, in inches?

49 inches

0

16 inches

0

24.5 inches

0

7 inches

CORRECT

14 inches

0

Explanation

We know that the formula for the area of a circle is πr_2. Therefore, we must set 49_π equal to this formula to solve for the radius of the circle.

49_π_ = _πr_2

49 = _r_2

7 = r

5

The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces. What is the approximate radius of the basketball?

3.06 inches

0

4.70 inches

CORRECT

5.43 inches

0

9.39 inches

0

14.75 inches

0

Explanation

To Find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get \[29.5\]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. (The information given of 22 ounces is useless)

6

A circle with center (8, **–**5) is tangent to the y-axis in the standard (x,y) coordinate plane. What is the radius of this circle?

5

0

8

CORRECT

16

0

4

0

Explanation

For the circle to be tangent to the y-axis, it must have its outer edge on the axis. The center is 8 units from the edge.