The length of the canvas, 1.1 m wide required to build a conical tent of height 14 m and floor area 346.5 m², is :

1. 490 m

2. 525 m

3. 665 m

4. 860 m

Given,

Height of cone, h = 14 m

Area of base floor = 346.5 m²

$\Rightarrow π\text{r}^2 = 346.5 \\[1em] \Rightarrow \dfrac{22}{7} \times \text{r}^2 = 346.5 \\[1em] \Rightarrow \text{r}^2 = \dfrac{346.5 \times 7}{22} \\[1em] \Rightarrow \text{r}^2 = \dfrac{2425.5}{22} \\[1em] \Rightarrow \text{r}^2 = 110.25 \\[1em] \Rightarrow \text{r} = \sqrt{110.25} \\[1em] \Rightarrow \text{r} = 10.5 \text{ m.}$

By formula,

l² = r² + h²

⇒ l² = 10.5² + 14²

⇒ l² = 110.25 + 196

⇒ l² = 306.25

⇒ l = $\sqrt{306.25}$ = 17.5 m

So, the total curved surface area of the tent = πrl

$= \dfrac{22}{7} \times 10.5 \times 17.5 \\[1em] = \dfrac{4042.5}{7} \\[1em] = 577.5 \text{ m}^2$

Let length of canvas be a m.

Area of canvas = Curved surface area of cone

⇒ a × b = 577.5

⇒ a × 1.1 = 577.5

⇒ a = $\dfrac{577.5}{1.1}$

⇒ a = 525 m

Hence, option 2 is the correct option.