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 4.00 per square metre, find the(i) inside surface area of dome,             (ii) volume of air inside the dome.

Answer 1

1. Given cost of white wash = 498.96 rupee 

cost of 1m2 area = 2 rupee

So inside surface area of dome = 498.96/2 = 249.48 m2

2. Let inner radius of the sphere = r

Now surface area of dome = 249.48

=> 2*Π*r2 = 249.48

=> 2*22/7 * r2 = 249.48

=> r2 = (249.48*7)/(2*22)

=> r2 = 1746.36/44

=> r2 = 39.69

=> r = √39.69

=> r = 6.3

Now volume of the air inside the dome = volume of the hemisphere dome

                                                         = (2/3)*Π*r3

                                                         = (2*22*6.3*6.3*6.3)/(3*7)    (Π = 22/7)

                                                         = 2*22*6.3*6.3*0.3

                                                         = 523.908 m3

So volume of the air inside the dome is  523.908 m3