All SAT Math Resources
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?
36
6
9
18
6
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?
Circle X
7
√12
6
4
6
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?
9.39 inches
4.70 inches
3.06 inches
5.43 inches
14.75 inches
4.70 inches
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?
5
4
16
8
8
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?
14 inches
49 inches
24.5 inches
16 inches
7 inches
7 inches
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.
To solve, simply realize that the radius is half the diameter. Thus, our answer is 12.
Example Question #361 : Plane Geometry
In the above diagram, and have lengths and , respectively. Give the radius of the circle.
The question cannot be answered with the information given.
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
In the above diagram, and have lengths and , respectively. Give the radius of the circle.
The question cannot be answered with the information given.
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.
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
In the above diagram, has length . Give the radius of the circle to the nearest whole number.
The question cannot be answered with the information given.
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.