Mensuration

Area = pi * r^2 = 25 * pi. Circumference = 2 * pi * r = 10 * pi. The ratio is (25 * pi) / (10 * pi) = 2.5. As a percentage, this is 250%.

Curved surface area of a cylinder = 2 * pi * r * h. Ratio = (2 * pi * r1 * h) / (2 * pi * r2 * h) = r1 / r2 = 3 / 2.

The area of a rectangle is calculated as length multiplied by width. Here, 4 cm * 3 cm = 12 cm^2.

The side length of a square is the square root of its area, so sqrt(576) = 24 cm. The diagonal of a square is side * sqrt(2), which is 24 * 1.414 = 33.936 cm, approximately 33.94 cm.

Let width = w, then length = w + 1. Perimeter = 2(l + w) = 2(w + 1 + w) = 14. So 2(2w + 1) = 14, which means 2w + 1 = 7, so 2w = 6, w = 3. Length = 4. Area = l * w = 4 * 3 = 12 cm^2.

The square's perimeter is 4 x 4.5 = 18 cm. A regular hexagon has six equal sides, so each side is 18/6 = 3 cm.

One hectare is 10,000 square meters, so the side of the square is 100m. The perimeter is 4 * 100 = 400m. For 15 rounds, the total wire length is 15 * 400 = 6000m.

Perimeter = 2(5x + 3x) = 16x = 64, so x = 4. Length = 20, Breadth = 12. Area = 240. Cost = 240 * 45 = 10800.

Area = 6000 / 0.25 = 24000 m^2. Let length = 5x, breadth = 3x. 15x^2 = 24000, x^2 = 1600, x = 40. Length = 200, breadth = 120. Perimeter = 2 * (200 + 120) = 640 m.

Side = 500 cm = 5 m. Area = side * side = 5 m * 5 m = 25 sq m.

Statement (I) gives the area of a square playground (1600), which allows calculating the side length (40) and thus the perimeter (160). Statement (II) gives the total cost (3200) and the rate per meter (20), allowing the perimeter to be calculated as 3200/20 = 160. Both statements independently provide sufficient information.

The cardboard area is 4 × 2 = 8 cm^2. The largest circle has diameter 2 cm, so its radius is 1 cm and its area is pi cm^2. The remaining area is 8 - pi cm^2.