Mensuration

Area = pi * r^2. Given r = 7 / sqrt(pi), Area = pi * (7 / sqrt(pi))^2 = pi * (49 / pi) = 49.

Area1 = pi * R^2 = 1386, R^2 = 1386 * 7 / 22 = 441, R = 21. Area2 = pi * r^2 = 962.5, r^2 = 962.5 * 7 / 22 = 306.25, r = 17.5. Width = R - r = 21 - 17.5 = 3.5.

Circumference = 2 * pi * r = 88. r = 88 / (2 * 22/7) = 14. Area = pi * r^2 = 22/7 * 14 * 14 = 22 * 28 = 616.

The largest circle inside a square has a diameter equal to the side of the square (21 cm). Radius r = 10.5 cm. Area = pi * r^2 = (22/7) * 10.5 * 10.5 = 22 * 1.5 * 10.5 = 346.5 sq cm.

Using the area of a circle formula, pi * r^2 = 3850, we find the radius r = 35 meters. The circumference is then calculated as 2 * pi * r = 2 * (22/7) * 35 = 220 meters.

Interpret the garbled wording as the cones having radii in the ratio 1:2 and equal height h = sqrt(3)r, where r is the smaller radius. Their slant heights are 2r and sqrt(7)r. Since curved surface area is proportional to radius x slant height, the ratio is 1:sqrt(7).

Area = pi * r^2 = 301.84. r^2 = 301.84 / 3.14 = 96.127. r = sqrt(96.127) = 9.8.

Area = (theta/360) * pi * r^2. Diameter = 20, so r = 10. Area = (63/360) * (22/7) * 100 = (7/40) * (22/7) * 100 = (1/40) * 22 * 100 = 2200/40 = 55.

Area of circle = pi * r^2. Sum of areas = pi * 5^2 + pi * 12^2 = pi * (25 + 144) = pi * 169. Since pi * R^2 = pi * 169, R^2 = 169, so R = 13.

If radius increases by 100%, new radius = 2r. New area = pi * (2r)^2 = 4 * pi * r^2. The increase is 4 * Area - Area = 3 * Area, which is 300%.

Circumference C = 2 * pi * r = 88. Thus, r = 88 / (2 * pi) = 14 m. Area = pi * r^2 = (22/7) * 14 * 14 = 616 m^2.

Area of circle 1 = pi * 3^2 = 9pi. Area of circle 2 = pi * 4^2 = 16pi. Sum = 25pi. The new circle has area pi * R^2 = 25pi, so R = 5.

Area of circle = pi * r^2 = 154. Using pi = 22/7, (22/7) * r^2 = 154, so r^2 = 154 * 7 / 22 = 7 * 7 = 49. Thus, r = 7 cm.

The area of a square is side^2. Given side^2 = 625, side = sqrt(625) = 25 m.

Area = pi * R^2 - pi * r^2 = pi * (7^2 - 5^2) = pi * (49 - 25) = 24 * pi.