Question

A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?

Answer 1

Internal radius of hemispherical bowl r = 15 cm

The volume of bowl  `= 2/3 pir^3`= volume of liquid 

 `= 2/3 pi(15)^3`

Volume of liquid = 2250 π cm³

Since, the liquid filled into the cylindrical shaped bottles of radius  `5/2 cm`and height 6 cm.

Let n be the no. of bottles.

Therefore,

The volume of liquid = n × volume of cylindrical shaped bottle

`2250pi = n xx pi xx (5/2)^2 xx 6`

`2250 = n xx 25 / 4 xx 6`

     `n  = (2250 xx 4)/(25 xx 6)`

      ` n = 60`

Hence, the no. of bottles = 60