SAT PRACTICE PROBLEMS ON CIRCLES

Problem 1 :

If the area of a circle is 64π, then the circumference of the circle is

(A) 8π      (B) 16π    (C) 32 π      (D) 64 π     (E) 128π

Solution

Problem 2 :

If the minute hand of a clock moves 45 degrees, how many minutes of time have passed?

(A) 6      (B) 7.5      (C) 15      (D) 30     (E) 36.5

Solution

Problem 3 :

If the circumference of a circle is 1, what is the radius of the circle?

(A) 1/2π      (B) 1/π      (C) 1/2      (D) π/2    (E) π

Solution

Problem 4 :

In the figure below, the ratio of the circumference of circle to the length of arc ADC is 8:1. What is the value of x ?

Solution

Problem 5 :

In the figure above, if the area of the circle with center is 100π and CA has a length of 6, what is the length of AB ?

(A) 2        (B) 3     (C) 4     (D) 5     (E) 6

Solution

Problem 6 :

In the figure below, is the center of the circle. If the area of triangle XOY is 25, what is the area of the circle?

(A) 25 π     (B) 25 π√2     (C) 50π     (D) 50π√3    (E) 625

Solution

Problem 7 :

Each of the 3 shaded regions above is a semicircle. If AB = 4, CD = 2 BC and BC = 2 AB, then the area of the entire shaded figure is 

(A) 28 π     (B) 42 π     (C) 84π     (D) 96π    (E) 168π

Solution

Problem 8 :

In the diagram below, if the circle with center A has an area of 72π, what is the area of the circle with center B?

(A) 18π   (B) 24π     (C) 30π      (D) 36π      (E) 48π

Solution

Problem 9 :

If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?

(A) 25%     (B) 50%     (C) 100%    (D) 125%    (E) 225%.

Solution

Problem 10 :

If an arc with a length of 12 π is 3/4 of circumference of a circle, what is the shortest distance between the endpoints of the arc?

(A) 4     (B) 4√2   (C) 8 π    (D) 8√2     (E) 16

Solution

Problem 11 :

The total area of the four equal circles in the figure above is 36π, and the circles are all tangent to one another. What is the diameter of the small circle?

Solution