Question

The sueface area of two spheres are in the ratio of 1:2. Then the ratio of there volume is ____?
(a)√2:1
(b)1:8
(c)1:2√2
(d)1:4
I want a simple step-by-step answer. ​

Answer 1

Answer:

b) 1:8

Step-by-step explanation:

Let the Surface areas be S1 and S2

S1:S2 = 1:2

So, we know the surface area of a sphere is 4πr²

Let the radius of the 2 spheres be r₁ and r₂

So,

4πr₁²: 4πr₂² = 1:2

r₁²: r₂² = 1:2

r₁:r₂ = 1:√2

Volume of a sphere = 4/3 πr³

So,

V₁:V₂ = 4/3 πr₁³: 4/3 πr₂³

V₁:V₂ = r₁³ : r₂³

V₁:V₂ = 1 : 8