What are the different way for solving the question for class 9^{th} question of Surface Areas and Volumes chapter of math of question no.8 of math please suggest me the best way for solving this question of exercise 13.8 A dome of a building is in the form of a hemi sphere. From inside, it was white-washed at the cost of Rs. 4989.60. If the cost of white-washing isRs20 per square meter, find the (i) inside surface area of the dome (ii) volume of the air inside the dome (Assume π = 22/7)

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# A dome of a building is in the form of a hemi sphere. From inside, it was white-washed at the cost of Rs. 4989.60. If the cost of white-washing isRs20 per square meter, find the (i) inside surface area of the dome (ii) volume of the air inside the dome (Assume π = 22/7) Q.8

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(i) Cost of white-washing the dome from inside = Rs 4989.60

Cost of white-washing 1m

^{2}area = Rs 20CSA of the inner side of dome = 498.96/2 m

^{2 }= 249.48 m^{2}(ii) Let the inner radius of the hemispherical dome be r.

CSA of inner side of dome = 249.48 m

^{2}(from (i))Formula to find CSA of a hemi sphere = 2πr

^{2}2πr

^{2}= 249.482×(22/7)×r

^{2 }= 249.48r

^{2 }= (249.48×7)/(2×22)r

^{2 }= 39.69r = 6.3

So, radius is 6.3 m

Volume of air inside the dome = Volume of hemispherical dome

Using formula, volume of the hemisphere = 2/3 πr

^{3}= (2/3)×(22/7)×6.3×6.3×6.3

= 523.908

= 523.9(approx.)

Answer: Volume of air inside the dome is 523.9 m

^{3}.