Question

a hemispherical dome open at the base is made from a sheet of fibre. if the radius of the hemispherical dome is 40cm and 13/170 of the fibre sheet actually used was wasted in making the dome, find the cost of the dome at the rate of rupees 35/- per 100cm square. (Take pie as 3.14)

Answer 1

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Here is ur answer-

Here,
r=40cm
Wasted sheet= 13/170 of the total sheet
Surface Are of dome=
$2\pi \: {r}^{2}$

Now ,
$2 \times 3.14 \times 40 \times 40$
$2 \times 314 \times 4 \times 4$
$314 \times 32$
$10048$

Surface Area of the Dome =10048cm2

Now Let the Area of fibre sheet =X
A.T.Q
$10048 +( 13 \div 170) \times x = x$
$10048 = x - (13 \div 170)x$
$10048 = (157 \div 170)x$
$x = 10880$
Now the Area of sheet required used =10880cm2
Cost of sheet used in making of dome=
$10880 \times 35 \div 100$
$1088 \times 3.5$
$3808$

Cost of making the Dome = ₹3808
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Answer 2

Answer:

Here is ur answer-

Here,

r=40cm

Wasted sheet= 13/170 of the total sheet

Surface Are of dome=

Now ,

Surface Area of the Dome =10048cm2

Now Let the Area of fibre sheet =X

A.T.Q

Now the Area of sheet required used =10880cm2

Cost of sheet used in making of dome=

Cost of making the Dome = ₹3808

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Step-by-step explanation: