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A hemispherical dome, open at the base is made from a sheet of fibre. If the radius of the hemispherical dome is 40cm and 13170 of the fibre sheet was wasted in making the dome, then find the cost of the dome at the rate of 35 per 100cm2 .

Answer
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Hint: Calculate the surface area of the hollow hemisphere and then use the rate of the fibre sheet to calculate the cost for the area of the hemisphere body to make. Use the relevant formula of hemisphere and not of sphere.

Complete step-by-step answer:
A hemispherical dome, open at the base is made from a sheet of fibre. If the radius of the hemispherical dome is 40cm and 13170 of the fibre sheet was wasted in making the dome at the rate of 35 per 100cm2 .
The formula for the surface area of the hemisphere is equal to 2πr2 .
As per given the radius of the hemisphere is equal to 40cm . Now calculate the volume of the hemisphere.
 A=2πr2=2×3.14×(40cm)2=10048cm2
The surface area of the hemisphere is equal to 10048cm2 .
Assume that the area of fibre sheet used is equal to x . As given that 13170 of the fibre sheet was wasted in making the dome. So,
 10048+13170x=x10048=x13170x10048=157170xx=10048×170157x=10880
As the total area of fibre sheet used in making the dome is equal to 10880cm2 .
The cost of a fibre sheet for each 100cm2 is equal to 35 rupees. The cost of fibre sheet for each 1cm2 is equal to 35100 rupees and the cost for 10880cm2 is equal to 35100×10880=3808 rupees.
So, the correct answer is “3808 Rs”.

Note: Out of the total sheet used in making the dome 13170 of the fibre sheet is wasted in making the dome and calculate the area of sheet that is used to make the dome only not the wastage part and find the cost for it.