The volumes of two spheres are in a ratio of 18 what is the ratio of their radii?

To find the ratio of the radii of two spheres when their volumes are in a given ratio, we can use the formula for the volume of a sphere:

V = (4/3)πr³

Let’s denote the radius of the first sphere as r₁ and the radius of the second sphere as r₂. According to the problem, the volumes of the two spheres are in a ratio of 18:

V₁ : V₂ = 18 : 1

Using the volume formula, we can express this ratio as:

(4/3)πr₁³ : (4/3)πr₂³ = 18 : 1

Since (4/3)π is common in both volumes, we can simplify it out:

r₁³ : r₂³ = 18 : 1

Now, to find the ratio of the radii, we take the cube root of both sides:

r₁ : r₂ = ∛18 : ∛1

Since ∛1 is simply 1, we can simplify the ratio to:

r₁ : r₂ = ∛18 : 1

Calculating ∛18 gives approximately 2.62. Hence, the ratio of the radii is about:

r₁ : r₂ ≈ 2.62 : 1

This means that the radius of the first sphere is about 2.62 times the radius of the second sphere.