Let the height of cylinder = h

volume of cylinder = pr²h

= p x 7 x 7 x h cm₃ = 49ph cm³

According to given condition

volume of hollow hemispherical shell = volume of solid cylinder

196/3 p = 49 p h. {From equatiion (1) and (2)}

Þ h= 196/3 x 49 = 4/3 cm.

Hence, height of the cylinder = 1.33 cm.


Example-16.A hemispherical bowl of internal radius 15cm containsa 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 ?

Solution : Volume of hemisphere= 2/3 pr³

Internal radius of hemisphere r = 15 cm

Volume of liquid contained in hemispherical bowl

= 2/3 p (15)³ cm³

= 2250 p cm³

This liquid is to be filled in cylindrical bottles and the height of each bottle (h) = 6 cm.and radius (R) = 5/2 cm

Volume of 1 cylindrical bottle = pRh²