Given
A cylinder has a height of 4 m and a radius of 1.5 m. What is the approximate radius of a sphere that has the same surface area as a cylinder?
[tex]\text{surface area of a cylinder= surface of area of sphere}[/tex][tex]2\pi r(r+h)=4\pi r^2[/tex]Given parameters
[tex]\begin{gathered} 2\times\pi\times1.5(1.5+4)=4\pi\times r^2 \\ 2\pi(5.5)=4\pi r^2 \\ 11\pi=4\pi r^2 \\ \text{divide both sides by 4}\pi \\ \frac{11\pi}{4\pi}=\frac{4\pi r}{4\pi}^2 \\ \frac{11}{4}=r^2 \\ \text{Take the square root of both sides} \\ r=\sqrt[]{\frac{11}{4}} \\ r=1.6583 \end{gathered}[/tex]The final answer
Option A
[tex]r=1.7m[/tex]