Question -
Answer -
(i) Cost ofwhite-washing the dome from inside = Rs 4989.60
Cost of white-washing1m2┬аarea = Rs 20
CSA of the inner sideof dome = 498.96/2 m2 ┬а= 249.48 m2
(ii) Let the innerradius of the hemispherical dome be r.
CSA of inner side ofdome = 249.48 m2┬а(from (i))
Formula to find CSA ofa hemi sphere = 2╧Аr2
2╧Аr2┬а=249.48
2├Ч(22/7)├Чr2┬а=249.48
r2┬а=(249.48├Ч7)/(2├Ч22)
r2┬а=39.69
r = 6.3
So, radius is 6.3 m
Volume of air insidethe dome = Volume of hemispherical dome
Using formula, volumeof the hemisphere = 2/3 ╧Аr3
=(2/3)├Ч(22/7)├Ч6.3├Ч6.3├Ч6.3
= 523.908
= 523.9(approx.)
Volume of airinside the dome is 523.9 m3.