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Q-- A dome of a building is in the form of hemisphere. from inside,it was white washed at the cost of ₹498.96. if the cost of white washing is ₹2.00 per sq m, find the1)inside surface area of dome2) volume of air inside dome.
Answers
Given:
Cost of white washing dome =498.96
Cost of white washing 1m
2
area = Rs.2
(i) CSA=
2
498.96
=249.48m
2
(ii) Let ratio =r, CSA =249.48cm
2
⇒249.48=2×
7
22
×r
2
........4πr
2
⇒r
2
=
44
249.48×7
=39.7m
2
⇒r=6.3m
Volume of air inside dome = Vol of hemispherical dome
=
3
2
πr
3
=
3
2
×
7
22
×6.3×6.3
=523.9m
3
Answer:
hey mate:-
Step-by-step explanation:
1. Given cost of white wash = 498.96 rupee
cost of 1m2 area = 2 rupee
So inside surface area of dome = 498.96/2 = 249.48 m2
2. Let inner radius of the sphere = r
Now surface area of dome = 249.48
=> 2*Π*r2 = 249.48
=> 2*22/7 * r2 = 249.48
=> r2 = (249.48*7)/(2*22)
=> r2 = 1746.36/44
=> r2 = 39.69
=> r = √39.69
=> r = 6.3
Now volume of the air inside the dome = volume of the hemisphere dome
= (2/3)*Π*r3
= (2*22*6.3*6.3*6.3)/(3*7) (Π = 22/7)
= 2*22*6.3*6.3*0.3
= 523.908 m3
So volume of the air inside the dome is 523.908 m3
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