Question

A circle is inscribed in a square. If the circumference of the circle increases by 10%, what is the percentage increase in the square's area?

a) 10%
b) 20%
c) 30%
d) 40%

Answer 1

When the circumference of a circle increases by 10%, the area of the square it is inscribed in will increase by 21%.

Step-by-step explanation:

When the circumference of a circle increases by 10%, the radius of the circle will also increase by 10% since the radius is half of the circumference. Since the circle is inscribed in a square, the length of the square's side will also increase by 10%.

The area of the square is calculated by multiplying the length of its side by itself, so when the length of the side increases by 10%, the area of the square will increase by [(1 + 10%)^2 - 1] * 100% = 21%.

Therefore, the percentage increase in the square's area is 21%, which is not one of the provided answer choices.