Question

How many metres of cloth of $1.1m$ width will be required to make a conical tent whose vertical height is $12m$ and base radius is $16m$? Find also the cost of the cloth used at the rate of $Rs.23$ per meter.

Answer 1

Given, $h=12m$ and $r=16m$
$\therefore$ $l=\sqrt{r^2+h^2}=\sqrt{{\left(16\right)}^2+{\left(12\right)}^2}=\sqrt{256+144}$
$=\sqrt{400}=20m$
$\therefore$ Curved surface area $=\pi rl$
$=\frac{22}{7}\times 16\times 20=\frac{7040}{7}{m}^2$
Width of cloth$=1.1m$
$\therefore$ Length of cloth required $=\frac{\frac{7040}{7}}{1.1}=\frac{70400}{77}=\frac{6400}{7}m$
$\therefore$ Cost of the cloth used @ Rs.$14$ per metre
$=$ Rs.$\frac{6400}{7}\times 14=$Rs.$12800$