Question : The shape of a petrol tank is shown in the figure. It has two hemispheres attached at two ends of a cylinder. Total length of the tank is 6 metres and the common diameter is 2 metres.
a) What is the length of the cylindrical part?
b) What is the volume of the cylindrical part?
c) What is the volume of the hemispherical part?
d) How many litres of the petrol does the tank contain?
Doubt by Krishna Kripa
Solution :
Total length of the Tank (H) = 6 m
Common diameter of cylinder and Hemisphere (D) = 2 m
Common Radius of the cylinder and Hemisphere = D/2 = 2/2 = 1 m
Common diameter of cylinder and Hemisphere (D) = 2 m
Common Radius of the cylinder and Hemisphere = D/2 = 2/2 = 1 m
a) What is the length of the cylindrical part?
Length of the cylindrical part (h)
= H-2r
= 6-2(1)
= 6-2
= 6-2(1)
= 6-2
= 4 m
b) What is the volume of the cylindrical part?
Volume of the cylindrical part (V1)
= πr²h
= π×(1)²×4
= 4π
= 4×(3.14)
= 12.56 m³
= π×(1)²×4
= 4π
= 4×(3.14)
= 12.56 m³
c) What is the volume of the hemispherical part?
Volume of the hemispherical part (V2)
=2×Volume of Hemisphere
=2×Volume of Hemisphere
[We have multiplied by 2 because there are two hemispheres]
= 2×(2/3)×πr³
= (4/3)π(1)³
= (4/3)π(1)
= (4/3)π
= 4π/3
= [4×3.14]/3
= 12.56/3
= 4.186
= 4.19 m³
(Rounded off up to two decimal places)
= (4/3)π(1)³
= (4/3)π(1)
= (4/3)π
= 4π/3
= [4×3.14]/3
= 12.56/3
= 4.186
= 4.19 m³
(Rounded off up to two decimal places)
d) How many litres of the petrol does the tank contain?
Total amount of petrol in the tank
= Volume of cylinder + Volume of Hemispheres
= V1+V2
= 12.56+4.19
= 16.75 m³
= V1+V2
= 12.56+4.19
= 16.75 m³
= 16.75×1000 [ ∵ 1m³ = 1000 litres]
= 16750 litres
= 16750 litres