Question

# A dome of a building is in the form of a hemisphere. From inside, it was white-washed, at the cost of Rs. $$498.96$$. If the cost of white-washing is $$Rs. 2.00$$ per square metre, find the (i) inside surface area of the dome(ii) volume of the air inside the dome.

Solution

## (i) We know thatArea whitewashed $$\times$$ Cost of white wash $$=$$ Total costArea whitewashed $$\times2=498.96$$Area whitewashed $$=\dfrac{498.96}{2}$$Area whitewashed $$=249.48\ m^2$$Now,Area of whitewashed is curved surface area of hemisphere (as only walls are whitewashed, not floor)Therefore,Inner surface area of dome $$=249.48\ m^2$$(ii) Volume of air inside dome $$=$$ Volume of hemisphere                                                  $$=\dfrac{2}{3}\pi r^3$$Let the radius of dome be 'r' mSurface area of dome $$=249.48\ m^2$$                              $$2\pi r^2=249.48$$              $$2\times\dfrac{22}{7}\times r^2=249.48$$                                $$r^2=39.69$$                                $$r=\sqrt{39.69}$$                                $$r=6.3\ m$$Volume of air inside the dome $$=$$ Volume of hemisphere                                                    $$=\dfrac{2}{3}\pi r^3$$                                                    $$=\dfrac{2}{3}\times\dfrac{22}{7}\times6.3^3$$                                                    $$=523.9\ m^3$$Mathematics

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