Question

conical tent is made of 4.5 m wide tarpaulin. Vertical height of the conical tent is 4 m and base radius is 3 m. Find the length of the tarpaulin used, assuming that 10% extra material is required for stitching margins and wastage in cutting (Take π = 3.14)

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Answer 1

Most probably your school text book or other popular mathematics text books. But similar question is there is NCERT too.

Width of the Tarpaulin = 4.5 m

Let it's length = (x) m

‘h’ of the tent = 4 m

‘r’ of the tent = 3 m

We know,

l (slant height) = √r² + h² = √3² + 4² = √9 + 16

⇒ l = √25 = 5 m.

Now, CSA of a right circular cone = πrl

∴ CSA = 3.14 × 3 m × 5 m = 15 m² × 3.14 = 47.1 m²

Real area of the tarpaulin = 10% of CSA + CSA

∴ Actual area of tarpaulin = 1/10 × 47.1 m² + 47.1 m²

⇒ Area = 4.71 + 47.1 m² = 51.81 m²

Now we know, area of a rectangle = l × b

∴ 4.5x = 51.81

⇒ x = 11.5133 m (Answer)