Question
Sun March 30, 2014 By: Amoolya Kamuni

A hemispherical dome, open,at base is made from a sheet of fibre, if diameter of hemispherical dome is 80cm and 13/170 of fibre sheet actually used was wasted in making the dome, then find the cost of dome at the rate of rupees 35 per 100 square cm.

Expert Reply
Mon March 31, 2014
Given, Diameter of the hemispherical dome = 80 cm
=> Radius of the hemispherical dome = 40 cm
 
We need to find the Curved Surface area of the hemispherical dome to find the cost of the sheet of the fibre.
 
Curved Surface Area of a hemisphere = 2 πr squared space equals space 2 cross times 3.14 cross times 40 cross times 40 space equals space 10048 space s q space c m
Let the area of the sheet of fibre used to make the dome = x sq cm
Since 13 over 170of the fibre sheet was wasted,
x minus w a s t a g e space equals space C. S. A space o f space t h e space d o m e x minus 13 over 170 x equals 10048 157 over 170 x equals 10048 x equals fraction numerator 10048 cross times 170 over denominator 157 end fraction equals 64 cross times 170 space equals 10880 s q space c m
 
Rate of the fibre sheet = Rs 35 per 100 sq cm
=> Cost of the sheet used to make the dome = 10880 cross times 35 over 100 equals R s space 3808
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