Dear Sir,

My son has asked me this question but I am somewhat lost. Can you please guide?
A vessel has the shape of an inverted cone.The radius of the top is 8 cm and the height is 20 cm. Water is poured in to a height of x cm.Show that if the volume of the water is V cubic cm,then V=(4/75)pi x3.

Thanks & regards,



The essential concept here is similar triangles.

In the diagram above I have let r be the radius of the circle formed by the water surface. The triangles PQR and PTS are similar and hence

 |QR|/|RP||TS|/|SP|  that is  8/20r/x 


r = 2/5  x

The volume of a cone of radius r and height h is

V = 1/3  r2 h

and hence the volume of water in your cone is

V = 1/3  r2 x =  1/3  ( 2/5  x)2 x =  4/75  x3