Question

If a sphere’s volume is doubled, what is the corresponding change in its radius?

Answer 1

The answer is the radius is increased ∛2 (≈ 1.26) times.

The sphere's volume formula is:
V = 4/3 π r³
where:
V - the sphere's volume,
r - radius of the sphere.

If sphere's volume is doubled, we have:
V₁ = 4/3 π r₁³
We need to know what is the ratio of r₁ and r.

V₁ = 2 × V = 2 × 4/3 π r³
⇒ 2 × 4/3 π r³ = 4/3 π r₁³
We can remove the same parts of the left and right sides of the equation:
2 × r³ = r₁³
r₁ = ∛(2 × r³)
r₁ = ∛2 × ∛r³
r₁ =∛2 × r
r₁ ≈ 1.26 r
Or: r₁/r = 1.26

Therefore, the radius is increased ∛2 (≈ 1.26) times.