Question

What length of trapezium 3m wide will be required to make conical
tent of height 8 cm and base radius 6m? Assume that extra length of
material that will be required for stitching margins and wastage in
cutting is approximately 20 cm (User-3.4)​

Answer 1

Answer:

answer is 63 m

Step-by-step explanation:

h=8

r=6m

b=3m

l=?

area of tapezium = csa / area of tent

cas of conical =πrl

l=√a-square+r-square= √8 square +√6square

=√64+√36=√100=10

l=10m

csa =πrl =22/7 ×6×10 =186 .4

l×b = 188.4

length = 188.4 /3 =62.8m

total length= 62.8m

and wastage of = 20cm =0.2cm

total length=62.8+0.2

=63 m .....

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 trapezium 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 trapezium required is 63 m.