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Answers
Step-by-step explanation:
Given :-
The internal and external radius of a hemispherical metallic vessel are 7 cm and
10.5 cm respectively. The density is 10 gm/cm³ .
To find :-
Find the weight of the vessel ?
Solution :-
Given that :
The internal radius of a hemispherical metallic vessel (r) = 7 cm
The external radius of a hemispherical metallic vessel (R) = 10.5 cm
Volume of a hemispherical vessel whose external and internal radii are R units and r units is (2/3)π(R³-r³) cubic units
=> Volume = (2/3)×(22/7)×(10.5³-7³) cm³
=> Volume = (2/3)×(22/7)×(1157.625-343)
=> Volume = (2/3)×(22/7)×814.625
=> Volume = (2×22×814.625)/(3×7)
=> Volume = 35843.5/21
=> Volume = 1706.83 cm³ (approximately)
Given that
Density of the vessel = 10gm/cm³
We know that
Density = Mass / Volume
=> Mass = Density×Volume
=> Mass = 10×1706.83 gm
=> Mass = 17068.3 gm
We know that 1kg = 1000g
=> Mass = 17068.3/1000
=> Mass = 17.0683 kg
=> Mass = 17.068 kg
Answer:-
The weight of the given hemispherical metallic vessel is 17068.3 gm or 17.068 kg
Used formulae:-
- Volume of a hemispherical vessel whose external and internal radii are R units and r units is (2/3)π(R³-r³) cubic units
- Density = Mass / Volume