PSAT Math : Circles
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Example Questions
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
√12
7
4
6
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 #61 : 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?
5.43 inches
14.75 inches
4.70 inches
3.06 inches
9.39 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 #5 : 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 #1 : Radius
A circle has an area of 
24.5 inches
14 inches
49 inches
7 inches
16 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 #1 : Radius
A certain circle has a circumference (in units) that is two times the area (in units squared). What is the radius of the circle?
The formula for the area of a circle is
The formula for the circumference of a circle is
Because the circumference is twice the area, your new formula is
You can divide both sides by 
Example Question #1 : Circumference Of A Circle
If a circle has an area of 
The formula for the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.
Example Question #1 : How To Find Circumference
A circle with an area of 13π in2 is centered at point C. What is the circumference of this circle?
13π
√26π
√13π
2√13π
26π
2√13π
The formula for the area of a circle is A = πr2.
We are given the area, and by substitution we know that 13π = πr2.
We divide out the π and are left with 13 = r2.
We take the square root of r to find that r = √13.
We find the circumference of the circle with the formula C = 2πr.
We then plug in our values to find C = 2√13π.
Example Question #1 : How To Find Circumference
A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?
25π
8π
6π
12π
10π
10π
First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10.
Circumference = π * diameter = 10π.
Example Question #1 : How To Find Circumference
A gardener wants to build a fence around their garden shown below. How many feet of fencing will they need, if the length of the rectangular side is 12 and the width is 8?
96 ft
8π + 24
4π + 24
40 ft.
8π + 24
The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π.
Example Question #1 : How To Find Circumference
The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?
5π
π√2.5
None of the other answers
π√5
2.5π
π√5
We first must calculate the distance between these two points. Recall that the distance formula is:√((x2 - x1)2 + (y2 - y1)2)
For us, it is therefore: √((4 - 2)2 + (6 - 5)2) = √((2)2 + (1)2) = √(4 + 1) = √5
If d = √5, the circumference of our circle is πd, or π√5.
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