Question

A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.

A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be filled into cylindrical-shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.

Answer 1

Inner diameter of the bowl = 30 cm

Inner radius of the bowl `=(30  "cm")/2= 15 "cm"`

Volume of liquid `= 2/3pir^3 =2/3xxpixx15^3 "cm"^3`

Radius of each bottle = 2.5 cm

Height = 6 cm

Volume of each bottl `=pir^2h = pixx5/2xx5/2xx6=(75pi)/2   "cm"^3`

total number of bottles required `=[(2/3pixx15xx15xx15xx6)/((75pi)/2)]= (2pixx15xx15xx15xx2)/(3xx75pi) = 15xx14=60`