Question

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of water

1. displaced out of the cylinder
2. left in the cylinder.  

Answer 1

We have,

Internal radius of the cylindrical vessel, `"R" = 10/2 = 5  "cm"`

Height of the cylindrical vessel, H = 10.5 cm,

Radius of the solid cone, `r = 7/2 = 3.5  "cm"`

height of the sollid cone, h = 6 cm

(i) Volume of water displaced out of the cylinder = Volume of the solid cone 

`= 1/3pi"r"^2"h"`

`= 1/3xx22/7xx3.5xx3.5xx6`

= 77 cm³ 

(ii) As,

Volume of the cylindrical vessel = πR²H

`= 22/7xx5xx5xx10.5`

= 825 cm³ 

So, the volume of water left in the cylindrical vessel = Volume of the cylindrical vessel

= 825 - 77

= 748 cm³