Question

John takes 2 hours to cut the grass in the lawn of a circular field. To cut the grass in a similar adjacent circular lawn of twice the radius, how many hours can John expect to take?

Answer 1

8

Explanation:

The area of a circle with twice the radius is 4 times the area of the smaller circle. If John's hours are proportional to area, we expect it will take him 4 times as long for the larger area.

John can expect to take 8 hours cutting the grass in the larger lawn.

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The area of a circle with radius r is ...

A = πr²

The area of a circle with radius 2r is ...

π(2r)² = 4πr² = 4A . . . . . 4 times the area of the smaller circle