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Q.

Choose the correct answer:


In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, then the quantity of juice which a person will get is


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a

135π c m 3  

b

117π c m 3  

c

99π c m 3  

d

36π c m 3   

answer is B.

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Detailed Solution

The correct answer is: 117π
We know,
volume of glass = volume of cylindervolume of hemisphere  
Volume of cylinder: V C =π r 2 h  
Volume of hemisphere: V H = 2 3 π r 3  
Radius of cylinder is 3 cm
Volume of cylinder:
VC=π (3) 2 15 VC=π×9×15 VC=135π c m 3  
 Volume of hemisphere:
VH=23π (3) 3 VH= 2 3 π×27 VH=2π×9 VH=18π c m 3  
Volume of glass= volume of cylinder – volume of hemisphere
volume of glass = 135π18π volume of glass = 117π c m 3  
The answer is option 2.
 
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