(Q6)A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?

Volume of hemisphere =
2
3
 πr3

Internal radius of hemisphere r = 15 cm

∴ Volume of liquid contained in hemispherical bowl =
2
3
 π( )3 cm3

  = π cm3

This liquid is to be filled in cylindrical bottles and the height of each bottle(h) = 6 cm

and the radius (R) =
5
2
 cm

∴ Volume of 1 cylindrical bottle = πR2h

= π × (
)2 ×
= π ×
× cm3 =
π cm3
Number of cylindrical bottles required =
Volume of hemispherical bowl
Volume of 1 cylindrical bottle
=
π
( / )π
 =
×
= .