A social welfare association supply drinking water for social affected people the drinking water is filled in water tank which is shape of cylinder with hemisphere end as shown in figure the whole lenght of tanker is 4.2m and the diameter of the base cylinder and two hemisphere are each 1.2m if they distributing drinking water to 60 people in a container each in shape of cylinder of radius 21cm and height 50cm find the quantity of water left in the container after distributing in litre​

Asked by shakilaalva31 | 18th Feb, 2020, 05:27: PM

Expert Answer:

Given:
Total height of the tank (H) = 4.2 m = 420 cm
Diameter of cylinder = 1.2 m = 120 cm = Diameter of cylinder
Radius of cylinder and hemisphere (r) V o l u m e space o f space t h e space tan k space equals space V o l u m e space o f space c y l i n d e r space plus space 2 cross times V o l u m e space o f space h e m i s p h e r e
equals πr squared straight h plus 2 cross times 2 over 3 πr cubed
equals πr squared straight h plus 4 over 3 πr cubed
equals 22 over 7 cross times 0.6 cross times 0.6 cross times 3 plus 4 over 3 cross times 22 over 7 cross times open parentheses 0.6 close parentheses cubed
equals 3.3942 plus 0.9051
equals 4.2993 space straight m cubed
space
Radius space of space container space left parenthesis straight r subscript 1 right parenthesis space equals space 21 space cm space equals space 0.21 space straight m
Height space of space container space left parenthesis straight h subscript 1 right parenthesis space equals space 50 space cm space equals space 0.5 space straight m
Volume space of space 1 space container space equals space straight pi open parentheses straight r subscript 1 close parentheses squared space straight h subscript 1 space equals space 22 over 7 cross times 0.21 cross times 0.21 cross times 0.5 equals 0.0693
Volume space of space 60 space containers space equals space 60 space cross times space 0.0693 space equals space 4.158 space straight m cubed
Quantity space of space water space left space in space the space tank space equals space Volume space of space tank space minus space volume space of space 60 space containers space equals space 0.1413 space straight m cubed
Since space 1 space straight m cubed space equals space 1000 space litres
rightwards double arrow Quantity space of space water space left space in space the space tank space equals space 141.3 space litres= Diameter/2 = 0.6 m = 60 cm
Height of the cylinder (h) = Total height - 2 x Radius of hemisphere = 4.2 - 1.2 = 3 m = 300 cm

Answered by Renu Varma | 24th Feb, 2020, 11:14: AM