Question : The radius of the base of a Conical tent is 12 m. The tent is 9 m high. Find the cost of canvas required to make the tent, if one square metre of canvas costs Rs. 120. (Take $\pi$ =3.14)
Option 1: Rs. 67,830
Option 2: Rs. 67,800
Option 3: Rs. 67,820
Option 4: Rs. 67,824
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Correct Answer: Rs. 67,824
Solution :
The lateral surface area of a cone,
$A = \pi r l$
where $r$ is the radius of the base, and $l$ is the slant height of the cone.
Given: $r = 12\operatorname{ m }$, and $h = 9\operatorname{ m}$
$l = \sqrt{r^2 + h^2} = \sqrt{12^2 + 9^2} = 15 \text{ m}$
⇒ $A = \pi \times 12 \times 15 = 565.2 \text{ m}^2$
Given that one square metre of canvas costs $ \text{Rs.}\; 120$.
The cost of the canvas required to make the tent would be $=565.2 \times 120 = \text{Rs.}\; 67824$
Hence, the correct answer is Rs. 67,824.
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