What length of tarpaulin 3 m wide will be required to make conical ten

1.	What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. (Use π = 3.14.)
Answer» ABC is a conical tent. Height, AO = h = 8 m. base radius, OC = r = 6 cm In ⊥∆AOC, AC² = AO² + OC² l² = (8)² +(6)² l² = 64 + 36 l² = 100 ∴ l = √100 l = 10 m Curved surface Area of cone C.S.A. = πrl = 3.14 × 6 × 10 = 188.4 m² Let the length of tarpaulin required be 1 m. In that 20 cm. (0.2 m) is wastage means remaining tarpaulin is (1 – 0.2 m) breadth, b = 3m ∴ Area of tarpaulin = curved surface area of tent. (l – 0.2 m) × 3 = 188.4 m² l - 0.2m = \(\frac{188.4}{3}\) l – 0.2 = 62.8 ∴ l = 62.8 + 0.2 ∴ l = 63 m.

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. (Use π = 3.14.)

Answer»

ABC is a conical tent.

Height, AO = h = 8 m.

base radius, OC = r = 6 cm

In ⊥∆AOC,

AC² = AO² + OC²

l² = (8)² +(6)²

l² = 64 + 36

l² = 100

∴ l = √100

l = 10 m

Curved surface Area of cone C.S.A. = πrl

= 3.14 × 6 × 10 = 188.4 m²

Let the length of tarpaulin required be 1 m.

In that 20 cm. (0.2 m) is wastage means remaining tarpaulin is (1 – 0.2 m)

breadth, b = 3m

∴ Area of tarpaulin = curved surface area of tent.

(l – 0.2 m) × 3 = 188.4 m²

l - 0.2m = \(\frac{188.4}{3}\)

l – 0.2 = 62.8

∴ l = 62.8 + 0.2

∴ l = 63 m.