Question

Question 112

A rectangular sheet of dimensions $25cm\times 7cm$ is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.

Answer 1

A rectangular sheet of dimensions $25cm\times 7cm$ is rotated about its longer side which makes a cylinder with base 25 cm and height 7 cm

Surface area of a base $=2\pi r$
$\therefore 2\pi r=25cm$
$\Rightarrow r=\frac{25\times 7}{2\times 22}=\frac{175}{44}cm$

Volume of a cylinder $=\pi r^{2}h$
$=\frac{22}{7}\times \frac{175}{44}\times \frac{175}{44}\times 7=\frac{175\times 175}{2\times 44}=\frac{30625}{88}=348.011c{m}^3$
Surface area = $2\pi rh=2\times \frac{22}{7}\times \frac{175}{44}\times 7$
$=\frac{44}{44}\times 175=175c{m}^2$