A hemispherical dome of a building and the walls of the cylindrical shaped building needs to be painted on inside. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, if the total height of the building is 9.8 m and cost of painting it is ₹2 per 100 cm2
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Solution :-
Circumference of the base = 17.6 m
Circumference of dome = 2πr
⇒ 17.6 = 2*22/7*r
⇒ 17.6*7 = 44r
⇒ r = 123.2/44
⇒ r = 2.8 m or 280 cm
Height of the cylindrical walls = 9.8 m - 2.8 = 7 m
Height = 7 m = 700 cm
CSA of dome + CSA of Cylindrical building = 2πr² + 2πrh
⇒ 2*22/7*280*280 + 2*22/7*280*700
⇒ 492800 cm² + 1232000 cm²
= 1724800 cm²
Total curved surface area = 1724800 cm²
Cost of painting = Rs. 2 per 100 sq cm
Total cost of painting = (1724800*2)/100
Total cost = Rs. 34496
Answer.
Circumference of the base = 17.6 m
Circumference of dome = 2πr
⇒ 17.6 = 2*22/7*r
⇒ 17.6*7 = 44r
⇒ r = 123.2/44
⇒ r = 2.8 m or 280 cm
Height of the cylindrical walls = 9.8 m - 2.8 = 7 m
Height = 7 m = 700 cm
CSA of dome + CSA of Cylindrical building = 2πr² + 2πrh
⇒ 2*22/7*280*280 + 2*22/7*280*700
⇒ 492800 cm² + 1232000 cm²
= 1724800 cm²
Total curved surface area = 1724800 cm²
Cost of painting = Rs. 2 per 100 sq cm
Total cost of painting = (1724800*2)/100
Total cost = Rs. 34496
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