Question

find the surface area of a cylinder with a height of 42 meters and a diameter that is one third its height. as you can see the question has already been answered my teacher wants me to show how she got the answer.

Answer 1

The height (h) of the cylinder is 42 meters.

Given that the diameter (d) of the cylinder is one third of its height,

$\begin{gathered} d=\frac{1}{3}h \\ d=\frac{1}{3}\times42 \\ d=14 \end{gathered}$

So the diameter of the cylinder is 14 meters.

Consider that the total surface area of a cylinder is given by,

$A=\pi d(\frac{d}{2}+h)$

Substitute the values,

$\begin{gathered} A=\pi(14)(\frac{14}{2}+42) \\ A=\pi(14)(49) \\ A=686\pi \end{gathered}$

Thus, option B is the correct choice.