Question

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?

Answer 1

The internal radius of the hemispherical bowl is 9cm. Therefore, the volume of the water in the hemispherical bowl is

`V = 2/3 pi xx (9)^3 cm^3`

The water in the hemispherical bowl is required to transfer into the cylindrical bottles each of radius`3/2`cm and height 4cm. Therefore, the volume of each of the cylindrical bottle is

`V_1 = pi xx(3/2)^2 xx 4 cm^3`

Therefore, the required number of cylindrical bottles is

`V = (2/3 pi xx (9)^3)/( pi xx(3/2)^2 xx 4)`

` = (2 xx (9)^3 xx (2)^2)/(3 xx (3)^2 xx 4)`

`= 54`

Hence No. of bottles = 54.