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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 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. - Mathematics

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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 6 m? 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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Solution

Height (h) of conical tent = 8 m

Radius (r) of base of tent = 6 m

Slant height (l) of tent`= sqrt(r^2+h^2)`

`=sqrt(6^2+8^2)m=sqrt100 m = 10m`

CSA of conical tent = πrl

= (3.14 × 6 × 10) m2

= 188.4 m2

Let the length of tarpaulin sheet required be l.

As 20 cm will be wasted, therefore, the effective length will be (l − 0.2 m).

Breadth of tarpaulin = 3 m

Area of sheet = CSA of tent

[(l − 0.2 m) × 3] m = 188.4 m2

l − 0.2 m = 62.8 m

l = 63 m

Therefore, the length of the required tarpaulin sheet will be 63 m.

Concept: Surface Area of a Right Circular Cone
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APPEARS IN

NCERT Class 9 Maths
Chapter 13 Surface Area and Volumes
Exercise 13.3 | Q 5 | Page 221

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