A conical tent of height 2.5 m with base area 36π m² is to be made by using tarpaulin. If the cost of tarpaulin is Rs 120 per square metre, then what is the total cost of constructing the tent?

Let r be the radius of the base of the tent.

Height (h) of the tent = 2.5 m

Base area of tent = 36π m²

⇒ πr² = 36π m²

⇒ r² = 36 m²

∴ r = 6 m

Now, slant height (l) of cone in given by $\sqrt{h^2+r^2}$.

$\Rightarrow l=\sqrt{2.5^2+6^2}=\sqrt{6.25+36}=6.5 \mathrm{m}$

The area of tarpaulin required to make conical tent is equal to the curved surface area of the cone.

C.S.A. of cone = $\mathrm{\pi rl}=\frac{22}{7}\times 6\times 6.5=122.57 {\mathrm{m}}^2$

Cost of 1 m² of tarpaulin = Rs 120

⇒ Cost of 122.57 m² of tarpaulin = Rs 120 × 122.57 = Rs 14708.40

Thus, the total cost of constructing the tent is Rs 14708.40.