Question

Find the surface area. Leave your answers in terms of π.cones 5A. 216π mi²B. 504π mi²C. 108π mi²D. 180π mi²

Answer 1

The figure below is a cylinder

The surface area of a cylinder is given as

Curved surface area of the cylinder + area of the circular top and bottom. So we have

`\begin{gathered} S.A=2\pi rh+\pi r^2+\pi r^2 \\ S.A=2\pi rh+2\pi r^2 \end{gathered}`

From the cylinder given

`\begin{gathered} height\text{ }h=9\text{ }mi \\ radius\text{ }r=(diameter)/(2)=(12)/(2)=6mi \end{gathered}`

So applying the formula, we have

`\begin{gathered} S.A=2\pi*6*9+2\pi*6^2 \\ =108\pi+72\pi \\ =180\pi\text{ }mi^2 \end{gathered}`

Hence the answer is option D. 180π mi²