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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 64 : 27
Concept
Use of basic formulae of sphere
Surface of Sphere = 4 x π x r2
Volume of Sphere = 4 / 3 x π x r3
Application
Let the radius of sphere A = x
Let the radius of sphere B = y
According to the question:
4 x π x x2 - 4 x π x y2 = 112π
(x - y) x (x + y) = 28
Putting the value of ( x + y ) = 14 ( Sum of radii of spheres)
(x - y) x (14) = 28
(x - y) = 2
Now
x + y = 14
x - y = 2
Upon solving
x = 8
y = 6
Ratio Volume of sphere = 4 π x3 : 4 π y3
83 : 63
512 : 216
64 : 27