Question

A social welfare association decides to supply drinking water for the flood affected people .the drinkink water is filled in a water tanker which is in the shape of a cylinder with hemispherical end as shown in figg .the whole length of the tanker is 4_2 m and the diameter of base of the cylinder and two hemisphere area each 1_2 m .If they distribute drinking water to 60 people in a container each is in the shapeof cylinder r=21 h = 50m find the quantity of water left in the tanker after distribution​

Answer 1

The process for finding the quantity of water left in the tank:

Here,  

Total height of the tank (h) = 4.2 m or 420 cm

Cylinder’s diameter = 1.2 m or 120 cm  

Radius of cylinder and hemisphere (r)

We know that,  

Volume of tank $= r^2 h + 2 \times \frac{2}{3} r^3$

$= r^2 h + \frac{4}{3} r^3$

$= \frac{22}{7} \times 0.6 \times 0.6 \times 3 + \frac{4}{3} \times \frac{22}{7} \times (0.6)^3$

$= 303942 + 0.9051$

= 4.2993 $m^3$

Radius of container () = 0.21 cm

Height of container ($h_1$) = 0.5 m

Volume of 60 containers

Quantity of water remaining in tank = volume of tank – volume of 60 containers  

= 0.1413 $m^3$

Since, 1 $m^3$ = 1000 liters.

Quantity of water remaining in the tank is 141.3 liters.

$\frac{Diameter}{2} = 0.6 \ m \ or \ 60 cm$

Height of the cylinder $= Total height - (2 \times Radius \ of \ hemisphere)$  

= 4.2 - 1.2

= 3 m or 300 cm