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A sphere with a radius of 6 cm has the same volume as a cylinder with a height of 4.5 cm. What is the radius of the cylinder

Verified Answer :

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\(\frac{4}{3} \pi r^3= \pi r^2h \\ \frac{4}{3}6^3\pi= \pi r^2(4.5)\\ 288\pi= \pi r^2(4.5)\\ \frac{288\pi}{4.5\pi}=r^2\\ 64 = r^2\\ \sqrt{64} = \sqrt{r^2}\\ 8=r\)

Answer;

radius of the cylinder = 8 cm

Explanation;

  • The volume of a sphere is given by 4/3πR³, while the volume of a cylinder is given by the formula πr²H.
  • Therefore; since the two volumes are equal, it means;

          4/3πR³= πr²H, cancelling out π, we get;

            4/3R³ = r²H

            4/3 × 6³ =r² × 4.5

            4/3 × 216 = 4.5 r²

              4.5 r² = 288

                 r² = 64

                 r = √ 64

                = 8 cm

The radius of the cylinder is thus, 8 cm

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