ISEE Word Problems Question 292: Answer and Explanation

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Question: 292

11. Use the diagram below to answer the question.

If the radius of the smaller circle is 6 cm and the radius of the larger circle is 10 cm, what is the area of the shaded region?

  • A. 16π cm2
  • B. 36π cm2
  • C. 64π cm2
  • D. 100π cm2

Correct Answer: C

Explanation:

C

To find the area of an irregularly shaped shaded region, find the areas of the two normal shapes and subtract the smaller from the larger. As the area of a circle is πr2, the area of the larger circle is 100π, and the area of the smaller circle is 36π. The difference is 64π.

You can estimate that the area is a fraction of the area of the larger circle (100π = approximately 300, as π is approximately 3). Estimate the values of the answer choices. Choice (A) is 48, which is too small. Choice (B) is 108, which might work. Choice (C) is 192, which might work. Choice (D) is the area of the larger circle, which is too big. While it may be difficult to determine whether the shaded region is about or of the larger circle, consider that farther out from the center takes up more ar

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