Question

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

Answer 1

Given a conical tent with

Height ( h ) = 8m

Radius ( r ) = 6m

So, its length = l2 = h2 + r2

= l2 = ( 8 )2m + ( 6 )m2

= l2 = 64m + 36m

= l2 = 100m

= l = 10m

Curved surface area of the cone = TTrl

= 3.14 x 6m x 10m

= 188.4 cm2

The extra length of material that will be required for stiching margins and wastages in cutting is approx 20 cm = 0.2m

So, its length = l - 0.2m

and its width = 3m

area of sheet = CSA of tent

so the area of the trapaulln = l x b

= ( l - 0.2m ) x 3m = 188.4m2

= l - 0.2m = 62.8m2

= l = 63m

Therefore, length of the trapaulin sheet required is 63m.

Answer 2

$\large{\mathcal{\underline{\:\:\:\:\:\:Solution\:\:\:\:\:\:\:\:}}}$

Hight of conical tent,h=8 m

Radius of base of tent,r=6 m

Stant height of tent, $\sf{l^2=r^2+h^2}$

__________________________

$\sf{Here,}$

$\large\sf{l^2=(6^2+8^2)}$

$\large\sf{→l^2=(36+64)}$

$\large\sf{→l^2=100}$

$\large\sf{→l=√100}$

$\large\sf{→l=10}$

__________________________

$\sf{Again,}$

CSA of conical tent,

$\large\sf{πrl}$

$\large\sf{=3.14×6×10}$

$\large\sf{=188.4\:m^2}$

__________________________

Let the length of tarpaulin sheet required be L

As, 20 cm will be wasted,therefore,

Effective length will be (L - 0.2 m)

Effective length will be (L - 0.2 m)Breadth of tarpaulin = 3 m (given)

_________________________

$\large\sf{Area\:of\:sheet\:=CSA\:of\:tent}$

$\large\sf{[(L-0.2)×3]=188.4}$

$\large\sf{L-0.2=\dfrac{188.4}{3}}$

$\large\sf{L-0.2=62.8}$

$\large\sf{L=62.8+0.2}$

$\large\sf{L=63}$

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