In the shortcut method, what percent of the square’s area corresponds to the circle’s area?

In the shortcut method, what percent of the square’s area corresponds to the circle’s area?

• A. 50%
• B. 78.5%
• C. 78.5% of the square
• D. 100%

Answer: (C)

When a circle fits exactly inside a square, the circle’s diameter equals the square’s side. If the square has side length L, the circle has radius R = L/2. The circle’s area is πR^2 = π(L/2)^2 = (π/4)L^2, while the square’s area is L^2. The ratio of circle area to square area is (π/4)L^2 ÷ L^2 = π/4 ≈ 0.785, i.e., about 78.5%. So the circle covers about 78.5% of the square’s area, expressed as 78.5% of the square. The phrasing “of the square” is important for clarity, hence the correct answer.

When a circle fits exactly inside a square, the circle’s diameter equals the square’s side. If the square has side length L, the circle has radius R = L/2. The circle’s area is πR^2 = π(L/2)^2 = (π/4)L^2, while the square’s area is L^2. The ratio of circle area to square area is (π/4)L^2 ÷ L^2 = π/4 ≈ 0.785, i.e., about 78.5%. So the circle covers about 78.5% of the square’s area, expressed as 78.5% of the square. The phrasing “of the square” is important for clarity, hence the correct answer.