SAT Math: Practice Questions-Additional topics in math-Circle theorems

Question

In the figure shown, point O is the center of the circle. One vertex of the square lies on the circle, and the opposite vertex is point O. If the area of the shaded region is 36\pi – 18, what is the perimeter of the square?

  1. 24
  2. 72
  3. 12\(\sqrt{2}\)
  4. 36\(\sqrt{2}\)
Answer/Explanation

Ans: C

Question

Segments \(\bar{OA}\) and \(\bar{OA}\) are radii of the semi circle above. Arc \(\widehat{AB}\) has length \(3\pi\) and \(OA=5\). What is the value of \(x\)? 

Answer/Explanation

Ans: 108

Question

The circumference of Earth is estimated to be 40,030 kilometers at the equator. Which of the following best approximates the diameter, in miles, of Earth’s equator? (1 kilometer ≈ 0.62137 miles)

  1. 3,205 miles
  2. 5,541 miles
  3. 7,917 miles
  4. 13,004 miles
Answer/Explanation

Ans: C

Question

The area enclosed by a circle is \(25\pi\) square inches. What is the length, in inches, of the radius of the circle? 

  1. 2.5
  2. 5
  3. 10
  4. 12.5
Answer/Explanation

Ans: B

Question

An instrument shows the number of revolutions per minute made by each tire of a car. In each revolution, the car travels a distance equal to the circumference of one of its tires. The circumference of each tire is equal to \(2 \pi r\), where \(r\) is the radius of the tire.

If the radius of each tire on Maria’s car is 0.30 meter, what is the approximate speed of Maria’s car, to the nearest kilometer per hour, when the instrument is showing 779 revolutions per minute? (1 kilometer = 1000 meters) 

Answer/Explanation

Ans: 88

Question

An instrument shows the number of revolutions per minute made by each tire of a car. In each revolution, the car travels a distance equal to the circumference of one of its tires. The circumference of each tire is equal to \(2 \pi r\), where \(r\) is the radius of the tire.

Maria gets new tires for her car. The radius of each of her old tires is 0.30 meter, and the radius of each of her new tires is 11% larger than the radius of one of her old tires. What is the circumference of each new tire, to the nearest tenth of a meter? 

Answer/Explanation

Ans: 2.1, 21/10

Question

In the figure above, the circle has center \(A\), and line segment \(CB\) is tangent to the circle at point \(C\). If \(AB\) = 1.0 and \(CB\) = 0.8, what is the length of the diameter of the circle? 

Answer/Explanation

Ans: 1.2, 6/5

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