Question

A dome of a building is in form of hemisphere .from inside it was white-washed at the cost of rs498.96 if the cost of white washing is rs2.00 per square metre .find the (1)inside surface area of the dome,(2)volume of the air inside the dome

Answer 1

HEY Buddy......!! here is ur answer

Given That... A dome of a building is in the form of hemisphere and we know that the volume of hemisphere = 2/3 πr³

And Total cost = 498.96 Rs.

(1) We Know that... Total cost = Area whitewash×cost of white wash

=> Area whitewashed = Total cost/cost of white wash

=> Area whitewashed = 498.96/2

=> Area whitewashed = 249.48 Rs.

And according to the question, the area whitewashed is Curved surface area of hemisphere.

Therefore, inner surface area of dome=298.48m²

(2) Let, the radius of the base of the dome =

Surface area of the dome = 249.48m²

According to the question....

2πr² = 249.48 m²

=> r² = 249.48/2π

=> r² = 249.48×7/2×22

=> r² = 39.69

=> r = √39.68 = 6.3 m

we know that... volume of inside the dome = volume of hemisphere

=> volume of inside the dome = 2/3πr³

=> 2/3×22/6×(6.3)³

=> 2/3×22/7×6.3×6.3×6.3

=> 523.908 m³ (approx.)

I hope it will be helpful for you...!!

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