Question

If a cylinder has the same radius and height as a sphere, then the ratio of their volume is

(i) 1:1 (ii) 3:4 (iii) 4:3 (iv) 3:2​

Answer 1

a + b = 10, ab = 16 Squaring,

(a + b)2 = (10)2

⇒ a2 + b2 + lab = 100

⇒ a2 + b2 + 2 x 16 = 100

⇒  a2 + b2 + 32 = 100

∴ a2 + b2 = 100 – 32 = 68

Now, a2 – ab + b2 = a2 + b2 – ab = 68 – 16 = 52

and a2 + ab + b2 = a2 + b2 + ab = 68 + 16 = 84