Question

A self help group wants to manufacture joke's caps of $3cm$ radius and $4cm$, height. If the available paper sheet is $1000c{m}^2$, then how many caps can be manufactured from that paper sheet?

Answer 1

Radius of the (conical) cap $=r=3cm$
height of the cap $=h=4cm$
Slant height $=l=\sqrt{r^2+h^2}$
$=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5cm$
Curved surface area of the cap $=\pi rl$
$=\frac{22}{7}\times 3\times 5=47.14c{m}^2$
Number of caps that can be made out of $1000c{m}^2=-\frac{1000}{47.14}=21.21$
$\therefore$ Number of caps $=21$