Question

What is the surface area of a cylinder with a radius of 25 mm and a height of 1 cm in square centimeters?

Answer 1

`\bf \textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=25~mm\\ \qquad 2.5cm\\ h=1~cm \end{cases}\implies SA=2\pi (2.5)(1+2.5) \\\\\\ SA=5\pi (3.5)\implies SA=17.5\pi \implies SA\approx 54.98~cm^2`

Answer 2

For this case we have that by definition, the surface area of a cylinder is given by:

`SA = 2 \pi * r * h + 2 \pi * r ^ 2`

We have as data that:

`h=1\cm\\`

`r = 25 \ mm = 2.5 \ cm`

Replacing the data we have:

`SA = 2 \pi * 2.5 * 1 + 2 \pi * (2.5) ^ 2`

`SA = 5\pi+12.5\pi`

`SA =17.5 \pi`

Taking
`\pi = 3.14`

`SA = 54.95 \ cm ^ 2`

ANswer:

`SA = 54.95 \ cm ^ 2`