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=(1)/(3)h \\ d=(1)/(3)*42 \\ 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((d)/(2)+h)`

Substitute the values,

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

Thus, option B is the correct choice.