Ice is formed in a container of the shape of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 3. 5cm and Height of the cone is 4cm. The ice is then put in a cylinderical glass full of juice such that on putting the ice the juice overflow. find the volume of juice left in the glass, if it's radius is 5cm and hieght 10. 5cm. (use π = 22/7)
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step 1 :- find volume of ice /
volume of ice = volume of right circular cone + volume of hemisphere
= πr²h/3 + 2/3 πr³
= πr²/ 3( h + 2r )
= 22/7 × (7/2)³ × 1/3 ( 4 + 2×7/2)
= 22/7 × 49/4 × 1/3 × 11
= 11/3 × 7/2 × 11 = 847/6 cm³
step 2:- find volume of cylindrical glass /
volume of cylindrical glass = πr²h
= 22/7 × (5)² × 10.5 = 22 × 25 × 1.5
= 550 × 1.5 = 825 cm³
step 3 :-
rest juice left in glass = volume of cylindrical glass - volume of ice cream
= (825 - 847/6 ) cm³
= ( 825× 6 -847)/6 cm³
=4103/6 cm³
=683.8667 cm³
volume of ice = volume of right circular cone + volume of hemisphere
= πr²h/3 + 2/3 πr³
= πr²/ 3( h + 2r )
= 22/7 × (7/2)³ × 1/3 ( 4 + 2×7/2)
= 22/7 × 49/4 × 1/3 × 11
= 11/3 × 7/2 × 11 = 847/6 cm³
step 2:- find volume of cylindrical glass /
volume of cylindrical glass = πr²h
= 22/7 × (5)² × 10.5 = 22 × 25 × 1.5
= 550 × 1.5 = 825 cm³
step 3 :-
rest juice left in glass = volume of cylindrical glass - volume of ice cream
= (825 - 847/6 ) cm³
= ( 825× 6 -847)/6 cm³
=4103/6 cm³
=683.8667 cm³
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