A circus tent is cylindrical to a height of $3$ meters and conical above it. If its diameter is $105\ m$ and the slant height of the conical portion is $53\ m$, calculate the length of the canvas $5\ m$ wide to make the required tent.
Given:
A circus tent is cylindrical to a height of $3$ meters and conical above it.
Its diameter is $105\ m$ and the slant height of the conical portion is $53\ m$.
To do:
We have to the length of the canvas $5\ m$ wide to make the required tent.
Solution:
Diameter of the cylindrical tent $= 105\ m$
This implies,
Radius $(r)=\frac{105}{2} \mathrm{~m}$
Height of the cylindrical part $(h_{1})=3 \mathrm{~m}$
Slant height of the conical portion $=53 \mathrm{~m}$
Therefore,
Total surface area of the tent $=\pi r l+2 \pi r h$
$=\pi r(l+2 h)$
$=\frac{22}{7} \times \frac{105}{2}(53+2 \times 3)$
$=165(53+6)$
$=165 \times 59$
$=9735 \mathrm{~m}^{2}$
Breadth of the canvas used $=5 \mathrm{~m}$
Length of the canvas used $=\frac{\text { Area }}{\text { Breadth }}$
$=\frac{9735}{5}$
$=1947 \mathrm{~m}$
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