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Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: Total surface area of a cylinder whose radius is 9 cm and height is equal to the side of a square of area 361 cm2. Quantity B: Area of a rectangle whose sides are in the ratio 5 : 4 and the perimeter is 2.5 times the perimeter of a semi-circle with area 308 cm2.

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: Total surface area of a cylinder whose radius is 9 cm and height is equal to the side of a square of area 361 cm2. Quantity B: Area of a rectangle whose sides are in the ratio 5 : 4 and the perimeter is 2.5 times the perimeter of a semi-circle with area 308 cm2. Correct Answer Quantity A < Quantity B

Quantity A:

Side of the square with area 361 cm2 = 19 cm;

∴ Height of the cylinder = 19 cm and radius is given as 9 cm;

∴ Total surface area of the cylinder = 2πr(r + h)

⇒ 2 × 22/7 × 9 × 28

⇒ 1584 cm2

Quantity B:

∵ the semi-circle has area 308 cm2;

½ πr2 = 308

⇒ r = 14 cm

Perimeter of the semicircle = πr + 2r

⇒ 36r/7

⇒ 72 cm

∴ Perimeter of the rectangle = 72 × 2.5 = 180 cm

∵ The ratio of sides of the rectangle is 5 : 4;

∴ Sides = 50 cm and 40 cm

∴ Area of the rectangle = 50 × 40 = 2000 cm2

∴ Quantity A < Quantity B

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