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

Melissa Norris

in Mathematics

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Tara Andrews on September 5, 2018

The answer is the radius is greater ∛2 (≈ 1.26) times.The sphere volume formula is:V = 4/3 pi r3where:V the volume of the sphere,r - radius of the sphere.If the sphere volume is doubled, we have:V₁ = 4/3 pi r₁3We need to know what is the ratio of r₁ and r.V₁ = 2 × V = 2 × 4/3 π r3⇒ 2 x 4/3 π r3 = 4/3 pi r₁3We you can delete the same parts of the left and right sides of the equation:2 × r3 = r₁3r₁ = ∛(2 × r3)r₁ = ∛2 × ∛r3r₁ =∛2 × rr₁ ≈ 1.26 rOr: r₁/r = 1.26 therefore, the radius is greater ∛2 (≈ 1.26) times.


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