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Question

The sum of the radii of spheres A and B is 14 cm. the radius of A being larger than that of B. The difference between their surface areas is 112π. What is the ratio of the volumes of A and B?

A 125: 64 Correct Answer Incorrect Answer
B 64:27 Correct Answer Incorrect Answer
C 27:8 Correct Answer Incorrect Answer
D 8:1 Correct Answer Incorrect Answer

Solution

Let the radius of the circle A be 'a' Let the radius of the circle B be 'b' Difference of the surface area of the circle is 112π 4 π a2 - 4 π b2 = 112 π (a + b).(a - b) = 28 a-b = 2 [Given,(a + b) = 2] a + b = 14 ....(1) a - b = 2 ....(2) Solving equation (1) and (2) ⇒ a = 8 and b = 6 So, Volume of sphere with radius a cm : volume of sphere with radius b cm = 4 π a : 4 π b ⇒ 83 : 63 ⇒ 512 : 216 ⇒ 64 : 27 ∴ The ratio of the volume will be 64 : 27

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