Question

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

Answer 1

`(4)/(3) \pi r^3= \pi r^2h \\ (4)/(3)6^3\pi= \pi r^2(4.5)\\ 288\pi= \pi r^2(4.5)\\ (288\pi)/(4.5\pi)=r^2\\ 64 = r^2\\ √(64) = √(r^2)\\ 8=r`

Answer 2

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