The length of canvas, 75 cm wide required to build a conical tent of height 14m and the floor area 346.5 m2 is

Base area = 346.5 $$m^2$$ = $$\pi r^2$$

=> $$r^2 = \frac{346.5 * 7}{22}$$

=> $$r = \sqrt{110.25} = 10.5 m$$

Height of tent = 14 m

Now, slant height$$(l)$$ of cone = $$\sqrt{r^2 + h^2}$$

=> $$l = \sqrt{10.5^2 + 14^2}$$

=> $$l = \sqrt{306.25} = 17.5m$$

Let length of cloth be $$x$$

Surface area of cone = $$\pi rl$$

=> $$0.75 * x = \frac{22}{7} * 10.5 * 17.5$$

=> $$x = \frac{22 * 10.5 * 17.5}{7 * 0.75}$$

=> $$x = 770m$$