Answer:
The cost of painting the hemispherical dome is 110880 unit
Step-by-step explanation:
Given as for a hemispherical dome :
The circumference of base = 17.6 m
The cost of painting it = 5 unit per 100 cm²
∵ circumference of base = circumference of circle = 2×[tex]\pi[/tex]×radius
So ,17.6 m = 2×[tex]\pi[/tex]×radius
Or, Radius = [tex]\frac{17.6\times 7}{2\times 22}[/tex]
Or, Radius = [tex]\frac{123.2}{44}[/tex] = 2.8 m
Or, R = 280 cm
So, Total surface area of hemispherical dome = 3×[tex]\pi[/tex]×radius²
or, Total surface area of hemispherical dome = 3×[tex]\pi[/tex]×280²
Or, Total surface area of hemispherical dome = [tex]\frac{3\times 22\times 280\times 280}{7}[/tex]
Or, Total surface area of hemispherical dome = [tex]\frac{5174400}{7}[/tex]
∴ Total surface area of hemispherical dome = 739200 cm²
Now, The cost of painting 100 cm² is 15 unit
So, The cost of painting 739200 cm² = [tex]\frac{15\times 739200}{100}[/tex]
Or, The cost of painting 739200 cm² = 110880 unit
Hence The cost of painting the hemispherical dome is 110880 unit Answer
