Question : How many metres of 2-m-wide cloth will be required to make a conical tent with a diameter of the base of 14 m and a slant height of 9 m ignoring wastage?
Option 1: 66 m
Option 2: 88 m
Option 3: 99 m
Option 4: 77 m
Correct Answer: 99 m
Solution :
Let the length of the 2 m wide cloth be $a$ metre.
Area of cloth = $2a$ m
2
Diameter of tent = 14 m
Radius of tent, $r$ = $\frac{14}{2}$ = 7 m
Slant height, $l$ = 9 m
The curved surface area of the cloth
= $\pi rl$
= $\frac{22}{7} \times7\times9$
= 198 m
2
Now, the Area of cloth = Curved surface area of the conical tent
⇒ $2a = 198$
$\therefore a = 99$ m
Hence, the correct answer is 99 m.
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