Question

A hemispherical tank full of water is emptied by a pipe at the rate of 3$\dfrac{4}{7}$ litres per second. How much time will it take to empty half the tank if its diameter is 3m? (take $\pi $ =$\dfrac{{22}}{7}$ )

Answer 1

Hint: When we come to know about 3D shapes such as cuboid, cube,cone,sphere,etc we might think about their various surface areas,volume and perimeter. Volume simply means how much space that 3D body can occupy . This is a very simple problem of Volume of 3D shape i.e., Hemi-Sphere.
Volume of Hemi-Sphere = $\dfrac{2}{3}\pi {r^3}$

Complete step by step answer:
Given- diameter of the hemispherical tank is 3m
So,radius (r) =$\dfrac{{Diameter}}{2}$ =$\dfrac{3}{2}$= 1.5 m
Now it is provided that the hemispherical tank full of water is emptied by a pipe at the rate of 3$\dfrac{4}{7}$ (=$\dfrac{{25}}{7}$ )litres per second, so 1 litre of water can be emptied in $\dfrac{7}{{25}}$ seconds.
(This is derived by a simple unit and dimension concept.)
Total volume of water = Volume of Hemi-Sphere = $\dfrac{2}{3}\pi {r^3}$
=$\dfrac{2}{3}\pi {(1.5)^3}$= 7.06858 m3 = 7.06858×1000 litres=7068.58 litres
(As we know that 1 ${m^3}$ = 1000 litres)
As, 1 litre of water is emptied from the tank in $\dfrac{7}{{25}}$ seconds.
Hence , 7068.58 litres of water can be emptied in 7068.58× $\dfrac{7}{{25}}$ seconds =1979.202 seconds

So,required time = 1979.202 seconds= $\dfrac{{1979.202}}{{60}}$ minutes = 32.986 minutes= 33 minutes (approximately)

Note: Proper care should be taken while conversion of units i.e. 1 min= 60 seconds , 1 ${m^3}$ = 1000 litres