Question

"Question 5 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]

Class 9 - Math - Surface Areas and Volumes Page 221"

Answer 1

Radius of the base (r) = 6 m
Height of the conical tent (h) = 8 m
Let l be the slant height of the cone.
∴ l = √h2 + r2 
⇒ l = √82 + 62 
⇒ l = √100 
⇒ l = 10 m
CSA of conical tent = πrl
                                = (3.14 × 6 × 10) m2 = 188.4 m2
Breadth of tarpaulin = 3 m
Let length of tarpaulin sheet required be x.
20 cm will be wasted in cutting.
So, the length will be (x - 0.2 m)
Breadth of tarpaulin = 3 m
Area of sheet = CSA of tent
[(x - 0.2 m) × 3] m = 188.4 m2
⇒ x - 0.2 m = 62.8 m
⇒ x = 63 m

Answer 2

Conical tents height ( h ) = 8 meter.

r = 6 meter.

.°. l = √ r² + h²

=> l = √ ( 6 )² + ( 8 )²

=> l = √ 36 + 64

=> l = √ 100

=> l = 10 meter

.°. csa of conical tent = πrl = 3.14 × 6 × 10

= 188.4 meter.

radius of Tripal = 3 meter

length of tripal = 188.4/3 = 62.8 meter.

wastage of cutting is approximately = 20 cm = 0.2 meter.

will need of total tipal is = 62.8 meter + 0.2 meter.

= 63 meter

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