Question

A hemispherical bowl of internal diameter 36 cm contains a liquid. This liquid is it to be filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

Answer 1

Given:

Hemispherical bowl with an internal diameter = 36 cm

Cylindrical bottle with radius = 3 cm and height = 6 cm

Find radius of hemisphere: r = `36/2`

= 18 cm

Volume of the hemispherical bowl

Volume(hemisphere) = `(2/3)·π·r^3`

= `(2/3)·π·18^3`

= 3888π cm³

Volume (bottle) = π.r².h

Volume (bottle) = π.3².6 = 54π

Number of bottles required = `"Volume(hemisphere)"/"Volume(one bottle)"`

= `(3888·π)/(54·π)`

= `3888/54`

= 72

72 bottles (assuming no loss of liquid)