The square that Krista cuts out of the circle with a 9-inch diameter has a diagonal of length equal to the diameter of the circle, which is 9 inches. The diagonal of the square can be calculated using the Pythagorean theorem:
diagonal^2 = side^2 + side^2 = 2(side^2)
side = diagonal / sqrt(2) = 9 / sqrt(2)
Therefore, the area of the square is:
area_square = side^2 = (9 / sqrt(2))^2 = 81 / 2 square inches
The area of the remaining piece is equal to the area of the circle minus the area of the square. The area of the circle can be calculated using the formula:
area_circle = pi * (diameter/2)^2 = pi * (9/2)^2
The area of the remaining piece is then:
area_remaining = area_circle - area_square
area_remaining = pi * (9/2)^2 - 81 / 2
area_remaining ≈ 37.7 square inches (rounded to the nearest tenth)
Therefore, the area of the remaining piece to the nearest tenth is 37.7 square inches.