ISEE Word Problems Question 269: Answer and Explanation

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Question: 269

3. Use the diagram to answer the question.

If the radius of Circle O is 6, what is the area of the shaded region?

  • A. 9π – 18
  • B. 9π – 36
  • C. 12π – 18
  • D. 36π – 36

Correct Answer: A

Explanation:

A

Questions seeking the area of a weird shaded region generally require you to subtract the area of one normal shape from the area of another normal shape. In this case, subtract the area of the triangle from the area of the quarter circle. The area of a quarter circle is πr2 = π(6)2 = 9π. As the triangle is a right triangle, the radii are also the base and height. The area of a triangle is bh = (6)(6) = 18. Choice (A) reflects the difference between the two areas.

You can estimate that the area is a small fraction of the area of the circle, which is 36π or approximately 108. Choices (B) and (C

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