Question:
A rectangular strip 25 cm × 7 cm is rotated about the longer side. Find The total surface area of the solid thus generated.
Solution:
Since the rectangular strip of $25 \mathrm{~cm} \times 7 \mathrm{~cm}$ is rotated about the longer side, we have:
Height, $h=25 \mathrm{~cm}$
Radius, $r=7 \mathrm{~cm}$
$\therefore$ Total surface area $=2 \pi r(r+h)=2 \pi(7)(25+7)$
$=14 \pi(32)$
$=448 \pi \mathrm{cm}^{2}$
$=448 \times \frac{22}{7} \mathrm{~cm}^{2}$
$=1408 \mathrm{~cm}^{2}$