How much cloth 2.5m wide will be required to make a conical tent … - Vidyadip

MCQ

How much cloth $2.5m$ wide will be required to make a conical tent having base radius $7m$ and height $24m?$

A
$180m$
B
$120m$
✓
$220m$
D
$550m$

✓

Answer

Correct option: C.

$220m$

Let the length of the required cloth be $L\ m$ and its breadth be $B\ m.$
Here, $B = 2.5m$
Radius of the conical tent $= 7m$
Height of the tent $= 24m$
Area of cloth required $=$ curved surface area of the conical tent
$\Rightarrow\text{L}\times\text{B}=\pi\text{rl}$
$\Rightarrow\text{L}\times\text{B}=\pi\text{rl}$
$\Rightarrow\text{L}\times2.5=\frac{22}{7}\times7\times\sqrt{7^2+24^2}$
$\Rightarrow2.5\text{L}=22\times\sqrt{49}+576$
$\therefore\text{L}=\frac{22\times25}{2.5}=220\text{m}$

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