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 r₁<span>³ We need to know what is the ratio of </span>r₁ and r.<span>
V</span>₁ = 2 × V = 2 × 4/3 π r³ ⇒ 2 × 4/3 π r³ = 4/3 π r₁<span>³ </span>We can remove the same parts of the left and right sides of the equation: 2 × r³ = r₁<span>³ </span>r₁ = ∛(<span>2 × r³) </span>r₁ = ∛2 × ∛<span>r³ </span>r₁ =∛2 × r r₁ ≈ 1.26 <span>r </span>Or: r₁/r = <span>1.26 </span> Therefore, the radius is increased ∛2 (≈ 1.26) times.
