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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 knowledge of Mathematics to choose between the possible answers. Quantity A: The circumference of two circles is 132 meters and 264 meters respectively. What is the difference between the area of larger circle and smaller circle? Quantity B: The semicircle having the area of 308 m2. If the circumference of a semicircle is equal to the length of rectangle and the width of the rectangle is equal to the perimeter of equilateral triangle with side value of 20 m. The area of the rectangle is ...

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 knowledge of Mathematics to choose between the possible answers. Quantity A: The circumference of two circles is 132 meters and 264 meters respectively. What is the difference between the area of larger circle and smaller circle? Quantity B: The semicircle having the area of 308 m2. If the circumference of a semicircle is equal to the length of rectangle and the width of the rectangle is equal to the perimeter of equilateral triangle with side value of 20 m. The area of the rectangle is ... Correct Answer Quantity A < Quantity B

Solving for Quantity A -

Circumference of larger circle = 264 m

Circumference of smaller circle = 132 m

For radius of smaller circle -

Circumference = 2πr

⇒ 132 = 2 × (22/7) × r

⇒ r = 21 m

For radius of larger circle,

⇒ 264 = 2 × (22/7) × R

⇒ R = 42 m

Area of smaller circle = πr2 = (22/7) × 21 × 21 = 1386 m2

Area of larger circle = πR2 = (22/7) × 42 × 42 = 5544 m2

Difference in Area = 5544 - 1386 = 4158 m2

Solving for Quantity B -

Area of semicircle = 308 m2

For radius of semicircle,

Area of semicircle = 308

⇒ πr2/2 = 308

⇒ r2 = 196

⇒ r = 14 m

Circumference of semicircle = πr + 2 * r = (22/7) × 14 + 2 * 14 = 72 m

Circumference of semicircle = length of rectangle = 72 m

For width of rectangle,

Perimeter of equilateral triangle = 3 × 20 = 60 m

Width of rectangle = 60 m

Area of rectangle = length × width = 60 × 72 = 4320 m2

∴ Quantity A < Quantity B

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