Question

A 3 inch by 4 inch rectangle is rotated about a corner. What is the maximum number of square inches in the area of the region touched by some point of the rectangle as it makes a full rotation? Express your answer in terms of pi.

Answer 1

25π square inches.

Explanation:

A 3-inch by 4-inch rectangle is rotated about a corner.

So, the maximum area that a point on the rectangle covers will be by the opposite corner point for 360° full rotation.

Now, the length of the diagonal is =
`\sqrt{3^(2) + 4^(2)} = 5` inches.

Therefore, the area of the circle will be calculated by 5 inches as the radius will be πr² = π(5)² = 25π square inches. (Answer)