Question

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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



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Answer 1

Answer:

63 m

Step-by-step explanation:

Since the tent is in a conical shape, the area of tarpaulin = the curved surface area of the cone.

The curved surface area of a right circular cone with base radius(r) and slant height(l) is πrl

where, Slant height, l = √(r2 + h2), h is the height of the cone.

The length of the tarpaulin can be calculated by dividing its area by its breadth.

Since the extra length of material = 20 cm, the actual length of the tarpaulin will be obtained by adding 20 cm to the length of the tarpaulin.

Radius, r = 6 m

Height, h = 8 m

Slant height, l = √r² + h²

= √(6)² + (8)²

= √36 + 64

= √100

= 10 m

Therefore, the curved surface area = πrl

= 3.14 × 6m × 10m

= 188.4 m2

Now, width of the tarpaulin = 3m

Area of the tarpaulin = 188.4 m2

So, Area of the tarpaulin = width of the tarpaulin × length of the tarpaulin

188.4 m2 = 3 × length of the tarpaulin

⇒ Length of the tarpaulin = 188.4 m2/3

= 62.8 m

Extra length of the material = 20cm = 20/100m = 0.2m

Actual length required = 62.8m + 0.2m = 63m

Thus, the required length of the tarpaulin is 63 m.

Answer 2

Answer:

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