Question

A hemispherical dome of a building needs to be painted. If the circumference of the base of the

Answer 1

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×$\pi$×radius

So ,17.6 m = 2×$\pi$×radius

Or, Radius = $\frac{17.6\times 7}{2\times 22}$

Or, Radius = $\frac{123.2}{44}$ = 2.8 m

Or, R = 280 cm

So, Total surface area of hemispherical dome = 3×$\pi$×radius²

or, Total surface area of hemispherical dome = 3×$\pi$×280²

Or, Total surface area of hemispherical dome = $\frac{3\times 22\times 280\times 280}{7}$

Or, Total surface area of hemispherical dome = $\frac{5174400}{7}$

∴ 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 = $\frac{15\times 739200}{100}$

Or, The cost of painting 739200 cm² = 110880 unit

Hence The cost of painting the hemispherical dome is 110880 unit  Answer