Question

A petrol tank is composed of cylinder with two hemispherical ends of equal

radii. If the total length of the tank is 6m and radius 1m, then find quantity of

water in litres can be filled in tank.​

Answer 1

Tank is in the shape of a cylinder with hemispheres of same radius attached to both ends.

Given : Length of the tank =6 m

Radius r=1 m is same for all shapes

Height of hemispheres = Radius (r)=1 m

∴ Height of the cylinder (h)=6−2=4 m

And radius of hemisphere =1 m

Now, volume of the tank = volume of two hemipheres + volume of a cylinder

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

                                          =$\pi (1)^{2} 4$ +  $\frac{2}{3}\pi 1^{3}$

                                          = 4π + 2 x  $\frac{2}{3}\pi$

                                          =4π + 2 x  $\frac{2}{3}\pi$

                                          =4π +  $\frac{4}{3}$$\pi$

                                           = $\frac{12+4}{3}\pi$

                                           =$\frac{16\pi }{3}$

                                            =16.75516 m  

                                           =16577.16 litres