Question

A conical tent is $10\text{m}$ high and the radius of its base is $24\text{m}$. Find
(i) slant height of the tent and
(ii) cost of the canvas required to make the tent, if the cost of $1{\text{m}}^2$ canvas is $\text{Rs}70$

Answer 1

Given:

$h=10\text{m}$
$r=24\text{m}$

(i) $l^2=h^2+r^2$ ...[Pythagoras theorem]

$l^2={\left(10\right)}^2+{\left(24\right)}^2$ $\Rightarrow$ $100+576$

$l=\sqrt{676}=26\text{m}$

(ii) Curved surface area $=\pi rl=\frac{22}{7}\times 24\times 26=\frac{13728}{7}$ ${\text{m}}^2$

Cost of $1{\text{m}}^2$ canvas $=\text{Rs}70$

Cost of $\frac{3728}{7}{\text{m}}^2$ canvas $=\frac{13728}{7}\times 70$

$=\text{Rs.}1,37,280$