A conical tent is \( 10 \mathrm{~m} \) high and the radius of its base is \( 24 \mathrm{~m} \). Find
(i) slant height of the tent.
(ii) cost of the canvas required to make the tent, if the cost of \( 1 \mathrm{~m}^{2} \) canvas is \( Rs.\ 70 \).
Given:
A conical tent is $10\ m$ high and the radius of its base is $24\ m$.
The cost of $1\ m^2$ canvas is $Rs.\ 70$.
To do:
We have to find the slant height of the tent and the cost of the canvas required to make the tent.
Solution:
Height of the conical tent $h= 10\ m$
Radius of the base $(r) = 24\ m$
Therefore,
Slant height of the tent $(l)=\sqrt{r^{2}+h^{2}}$
$=\sqrt{(24)^{2}+(10)^{2}}$
$=\sqrt{576+100}$
$=\sqrt{676}$
$=26 \mathrm{~m}$
The curved surface area of the conical tent $=\pi r l$
$=\frac{22}{7} \times 24 \times 26$
Rate of $1 \mathrm{~m}^{2}$ canvas used $=Rs.\ 70$
This implies,
The total cost of the tent$=Rs.\ \frac{22}{7} \times 24 \times 26 \times 70$
$= Rs.\ 137280$
Therefore,
The slant height of the tent and the total cost of the tent used are $26 \mathrm{~m}$ and $Rs.\ 137280$ respectively.
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