Mensuration

Volume = pi * r^2 * h. Using pi = 3.14, r = 5.8, h = 21.4: 3.14 * 33.64 * 21.4 is approximately 2260.

Surface area of a sphere is 4 * pi * r^2. Ratio = (4 * pi * 1^2) / (4 * pi * 2^2) = 1 / 4.

Original radius = 3, new radius = 6. Surface area = 4 * pi * r^2 = 4 * 3.14 * 6^2 = 4 * 3.14 * 36 = 452.16.

Curved surface area = pi * r * l = 423.9. 3.14 * 9 * l = 423.9, so l = 423.9 / 28.26 = 15. Height h = sqrt(l^2 - r^2) = sqrt(225 - 81) = sqrt(144) = 12. Volume = (1/3) * pi * r^2 * h = (1/3) * 3.14 * 81 * 12 = 3.14 * 81 * 4 = 1017.36.

Volume of sphere = 4/3 * pi * r^3 = 4/3 * pi * 8 = 32/3 * pi. Volume of cylinder = pi * r^2 * h = pi * 4 * h. Equating: 32/3 * pi = 4 * pi * h. h = 32/12 = 8/3 = 2.67 cm.

Volume of sphere is (4/3)pi*r^3 and volume of cone is (1/3)pi*r^2*h. Setting them equal: (4/3)pi*r^3 = (1/3)pi*r^2*h. Dividing both sides by (1/3)pi*r^2 gives 4r = h.

1 cm = 10 mm, so 1 cm^2 = 100 mm^2. Therefore, 15 cm^2 = 15 * 100 = 1500 mm^2.

Volume of a cylinder = pi * r^2 * h. Using pi = 22/7, Volume = (22/7) * 3^2 * 21 = 22 * 9 * 3 = 594.

The wording asks for a prism height, but the object is a square-based pyramid. Using pyramid volume, 250 = (1/3)(5^2)h, which gives h = 30 cm.

Radius r = 6. r + h = 38, so h = 32. Total Surface Area = 2 * pi * r * (r + h) = 2 * pi * 6 * 38 = 456 * pi. Using pi = 3.14159, 456 * 3.14159 = 1432.56. The closest option is 1431.84.

Area = pi * R^2 = pi * (10^2 + 24^2) = pi * (100 + 576) = pi * 676. R = sqrt(676) = 26.

Area = pi * r^2 = 3.14 * 8 * 8 = 3.14 * 64 = 200.96.

Area = pi * r^2 = 3.14 * (4.5)^2 = 3.14 * 20.25 = 63.585. Rounding to one decimal place gives 63.6.