A juice seller serves his customers using glasses that are cylindrical in shape, with a raised hemispherical bottom.The inner diameter of the cylindrical glass is 7 cm and height 12 cm. The bottom of the glass has a raised hemispherical portion. Find the apparent and actual capacities of the glass.

Asked by Topperlearning User | 27th Oct, 2017, 02:00: PM

Expert Answer:

 

begin mathsize 12px style Inner space radius space of space the space glass space left parenthesis straight r right parenthesis space equals 7 over 2 space cm
Height space left parenthesis straight h right parenthesis space equals space 12 space cm
Apparent space capacity space of space the space glass space equals space πr squared straight h
equals 22 over 7 cross times 7 over 2 cross times 7 over 2 cross times 12
equals 462 space cm cubed
Volume space of space the space inverted space hemispherical space bottom space equals space 2 over 3 πr cubed
equals 2 over 3 cross times 22 over 7 cross times 7 over 2 cross times 7 over 2 cross times 7 over 2
equals space 539 over 6 space cm cubed
Actual space capacity space of space the space glass space equals space 462 space minus space 539 over 6
equals space 372 1 over 6 space cm cubed
Apparent space capacity space of space the space glass space equals space 462 space cm cubed
Actual space capacity space of space the space glass space equals space 372 1 over 6 space cm cubed
end stylebegin mathsize 12px style Inner space radius space of space the space glass space left parenthesis straight r right parenthesis space equals 7 over 2 space cm
Height space left parenthesis straight h right parenthesis space equals space 12 space cm
Apparent space capacity space of space the space glass space equals space πr squared straight h
equals 22 over 7 cross times 7 over 2 cross times 7 over 2 cross times 12
equals 462 space cm cubed
Volume space of space the space inverted space hemispherical space bottom space equals space 2 over 3 πr cubed
equals 2 over 3 cross times 22 over 7 cross times 7 over 2 cross times 7 over 2 cross times 7 over 2
equals space 539 over 6 space cm cubed
Actual space capacity space of space the space glass space equals space 462 space minus space 539 over 6
equals space 372 1 over 6 space cm cubed
Apparent space capacity space of space the space glass space equals space 462 space cm cubed
Actual space capacity space of space the space glass space equals space 372 1 over 6 space cm cubed
end style

Answered by  | 27th Oct, 2017, 04:00: PM