Question

A hemispherical dome is constructed on a building at the rate of Rs.18 per sq.m. of the outer CSA. If the total cost of construction of the dome is Rs. 1386. Find the volume of space occupied by the dome?

Answer 1

given the cost for constructed is 1386
at the rate of 18 per m.sq
so,
1386/18=77
so the CSA is 77
we know that CSA of hemisphere is 2πr²
so...
2πr²=77
2×22÷7×r²=77
r²=77×7/2×22
r²=49/4
r=√49/4
r=7/2
r=3.5

now volume hemisphere is 2/3πr³
then substitute the r=3.5
2/3×22/7×3.5³
2/3×3.14×42.875
volume=89.751

Answer 2

Given that cost of construction = 1386 rs
and the rate is 18 rs per sq.m.
so, the CSA of hemisphere dome = 1386/18
=77 m
CSA of hemisphere dome = 2/3 π r²
77 m= 2π r²
77 ×7/2×22 = r²
539/44
49/4 = r²
7/2 = r
r= 3.5 m
volume of hemisphere dome = 2/3 π r3
where r= 3.5
so, volume = 2/3 × 22/7 ×( 3.5 )³
=89.83 m³.
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