"Question 8 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 meter, find the (i) inside surface area of the dome, (ii) volume of the air inside the dome.
Class 9 - Math - Surface Areas and Volumes Page 236"
Answers
VOLUME:
The space occupied by an object solid body is called the volume of the particular object solid body volume is always measured in cubic unit.
Surface area:
Surface area of a solid object is a measure of the total area that the surface of the object occupies and it is always measured in square unit.
Hemisphere:
When
a plane through the centre of a sphere divides the sphere into 2 equal parts
then these two equal parts are called hemisphere
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Given, cost of white washed=₹ 498.96
& Cost of white washing per sq m= ₹ 2
(i) Inside surface area of the dome =Total cost of white washed / cost of white washing per sq m
= (498.96/2.00)
= 249.48 m²
Inside surface area of the dome =249.48 m²
(ii) Let r be the radius of the dome.
Inside Surface area of hemisphere= 2πr²
2 × 22/7 ×r²= 249.48
r²= (249.48×7)/(2×22)
r² = 39.69
r= √39.69
r = 6.3m
Volume of the air inside the dome = Volume of the dome
= 2/3πr³
= (2/3 × 22/7 × 6.3 × 6.3 × 6.3)
= 523.908 m³ (approx.)
Volume of the air inside the dome =523.908 m³ (approx.)
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Hope this will help you....