SAT Math : Circles

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Find The Length Of A Radius

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

 

Possible Answers:

36

6

9

18

Correct answer:

6

Explanation:

We know that the formula for the area of a circle is πr2. Therefore, we must set 36π equal to this formula to solve for the radius of the circle.

36π = πr2

36 = r2

6 = r

Example Question #1 : How To Find The Length Of A Radius

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

 

 

Possible Answers:

7

√12

6

4

Correct answer:

6

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 

 

Example Question #2 : How To Find The Length Of A Radius

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? 

 

Possible Answers:

9.39 inches

4.70 inches

3.06 inches

5.43 inches

14.75 inches

Correct answer:

4.70 inches

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) 

 

Example Question #3 : How To Find The Length Of A Radius

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? 

Possible Answers:

5

4

16

8

Correct answer:

8

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.

Example Question #3 : How To Find The Length Of A Radius

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

Possible Answers:

14 inches

49 inches

24.5 inches

16 inches

7 inches

Correct answer:

7 inches

Explanation:

We know that the formula for the area of a circle is πr2. Therefore, we must set 49π equal to this formula to solve for the radius of the circle.

49π = πr2

49 = r2

7 = r

Example Question #111 : Circles

Find the radius of a circle given the diameter is 24.

Possible Answers:

Correct answer:

Explanation:

To solve, simply realize that the radius is half the diameter. Thus, our answer is 12.

Example Question #361 : Plane Geometry

Chords

In the above diagram,  and  have lengths  and , respectively. Give the radius of the circle.

Possible Answers:

The question cannot be answered with the information given.

Correct answer:

Explanation:

If two chords of a circle intersect, the measure of the angles they form is equal to half the sum of the measures of the angles they intercept that is, 

The ratio of the measures of arcs on the same circle is equal to that of their lengths, so

and 

Substituting:

 if  is the circumference of the circle, and the length of the arc  is ,

 has length  and measure  so

or

Since, if the radius is ,

Solve for :

 

Example Question #362 : Plane Geometry

Secant

In the above diagram,  and  have lengths  and , respectively. Give the radius of the circle.

Possible Answers:

The question cannot be answered with the information given.

Correct answer:

Explanation:

The ratio of the degree measures of the arcs is the same as that of their lengths. Therefore, 

and 

If a secant and a tangent are drawn to a circle from a point outside the circle, the measure of the angle they form is equal to half the difference of the measures of their intercepted arcs; therefore, 

Substituting:

Since  has length , then, if we let  be the circumference of the circle,

Divide the circumference by  to obtain the radius:

Example Question #61 : Radius

Give the radius of a circle with diameter fifteen yards.

Possible Answers:

Correct answer:

Explanation:

Convert fifteen yards to inches by multiplying by 36:

The radius of a circle is one half its diameter, so multiply this by :

Example Question #361 : Sat Mathematics

Tangents

In the above diagram,  has length . Give the radius of the circle to the nearest whole number.  

Possible Answers:

The question cannot be answered with the information given.

Correct answer:

Explanation:

Call . The measure of the corresponding major arc is  

If two tangents are drawn to a circle from a point outside the circle, the measure of the angle they form is equal to half the difference of the measures of their intercepted arcs; therefore

Substituting:

Therefore, . Since  has length , it follows that if  is the circumference of the circle, 

Divide the circumference by  to obtain the radius:

.

This makes 47 the correct choice.

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