Question

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of RS 997.92. If the cost of white washing is RS 400 paisa per square metre, find the(i) inside surface area of dome,             (ii) volume of air inside the dome.

Answer 1

the cost of white washing =rs.997.92
cost of white washing per area =400 paisa=rs 4
therefpore inner area of dome=997.92/4=249.48 sq.m
volume of the hemishere=$2/3 \pi r ^{3}$
area =$2 \pi r^{2}$=249.48
so $r^{2}$=249.48/2$\pi$
r=6.30m
volume =$2/3 \pi 6.30 ^{3}$=523.43m$^{3}$

Answer 2

Answer:

Step-by-step explanation:

cost of white washing =rs.997.92

cost of white washing per area =400 paisa i.e. 400/100= Rs 4

We know that,

Total cost=Inner Total area * Rate per metre square.

997.92=Area * 4

Inner area =997.92/4=249.48 sq.m

ii, Now,

volume of the hemisphere=2/3pi r^3

area =2pi r^{2} =249.48

so r^{2} =249.48/2pi

r^2=39.69

r=6.30m

volume =2/3 pi * 6.30 ^{3} =523.43m ^{3}