The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
27:1
1:27
1:9
9:1
Explanation:
the ratio between the radii of two spheres is 1 : 3.
we know, volume of sphere = 4/3 πr³
⇒volume of sphere ∝ (radius)³
so, volume of sphere₁/volume of sphere₂ = (r₁/r₂)³
= (1/3)³
= 1³/3³
= 1/27
hence ratio of volume of spheres is 1 : 27.
the ratio between the radii of two spheres is 1 : 3.
we know, volume of sphere = 4/3 πr³
⇒volume of sphere ∝ (radius)³
so, volume of sphere₁/volume of sphere₂ = (r₁/r₂)³
= (1/3)³
= 1³/3³
= 1/27
hence ratio of volume of spheres is 1 : 27.