A vessel in the form of an inverted cone is filled with water to the brim Its height is 20 cm and di...

Question

A vessel in the form of an inverted cone is filled with water to the brim. Its height is 20 cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one-third of the water in the original cone overflows.

What is the volume of each of the solid cone submerged?

Accepted Answer

Solution Assume that a cone has a height of h and a circular base with radius r This cone will have a volume that is onethird of the product of the bases area and its height Given height of the cone h 20 cm Diameter of the cone 168 cm Radius of the cone r 1682 84 cm Volume of water in the vessel 13 rsup2suph 13 x84sup2sup x20 13x227x84 x84 x20 14784 cmsup3sup One third of volume of water in the vessel 13 14784 4928 cmsup3sup One third of volume of water in the vessel Volume of water over flown Volume of water over flown volume of two equal solid cones dropped into the vessel volume of two equal solid cones dropped into the vessel 4928 cmsup3sup Volume of one solid cone dropped into the vessel 49282 2464 cmsup3sup Hence the volume of each of the solid cone submerged is 2464 cmsup3sup

ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration