Question

If the volume of two spheres is in the ratio 27 ∶ 64, then the ratio of their radii is ______.

पर्याय

• 3 : 4

• 4 : 3

• 9 : 16

• 16 : 9

Answer 1

If the volume of two spheres is in the ratio 27 ∶ 64, then the ratio of their radii is 3 : 4.

Explanation:

Let the radius of sphere 1 be r₁, and the radius of sphere 2 be r₂

`"Volume of sphere 1"/"Volume of sphere 2" = (4/3 πr_1^3) /(4/3 πr_2^3) = r_1^3/ r_2^3`

Now,

`27/64 = r_1^3/r_2^3`

`(r_1/r_2)^2 = (3/4)^3`

`r_1/r_2 = 3/4`

r₁ : r₂ = 3 : 4