The outer radius of a circular path is 3 m greater than its inner radius. If the area of the path is 75π square metres, what is the inner radius?
Answer and explanation
Correct answer: 11 m
Let the inner radius be r metres. Then the outer radius is (r+3) metres. The area of the path is π[(r+3)^2−r^2] = 75π. Cancelling π gives (r+3)^2−r^2 = 75, so 6r+9=75 and r=11. Therefore, option B, 11 m, is correct. Exam tip: For a circular path, use π[(outer radius)^2−(inner radius)^2], not the area of the outer circle alone.
Frequently asked questions
What is the correct answer to this question?
11 m
Why is this the correct answer?
Let the inner radius be r metres. Then the outer radius is (r+3) metres. The area of the path is π[(r+3)^2−r^2] = 75π. Cancelling π gives (r+3)^2−r^2 = 75, so 6r+9=75 and r=11. Therefore, option B, 11 m, is correct. Exam tip: For a circular path, use π[(outer radius)^2−(inner radius)^2], not the area of the outer circle alone.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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