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A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 4989.60. If the cost of white-washing is Rs 20 per square metre, find the (ii) volume of the air inside the dome.

Q : 8    A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of \small Rs\hspace{1mm}4989.60. If the cost of white-washing is Rs 20 per square metre, find the

(ii) volume of the air inside the dome. 

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Let the radius of the hemisphere be r\ m

Inside the surface area of the dome = 249.48\ m^2

We know, Surface area of a hemisphere = 2\pi r^2

\\ \therefore 2\pi r^2 = 249.48 \\ \Rightarrow r^2 = \frac{249.48\times7}{2\times22} \\ \Rightarrow r = 6.3\ m

\therefore  The volume of the hemisphere = \frac{2}{3}\pi r^3

= \frac{2}{3}\times\frac{22}{7}\times (6.3)^3

= 523.908\ m^3

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