Question

A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm × 14 cm × 10.5 cm. Find the rise in the level of the water when the solid is submerged.

Answer 1

Diameter of cylindrical container = 42 cm 

Therefore, radius (r) = 21 cm

Dimensions of rectangular solid = 22 cm × 14 cm × 10.5 cm 

Volume of solid = 22 × 14 × 10.5 cm³  ...(1) 

Let height of water = h 

Therefore, volume of water in the container = πr²h 

= `22/7 xx 21 xx 21 xx h  cm^3`

= 22 × 63h cm³  ...(2) 

From (1) and (2)   

22 × 63h = 22 × 14 × 10.5 

`=> h = (22 xx 14 xx 10.5)/(22 xx 63)` 

`=> h = 7/3` 

`=> h = 2 1/3` or 2.33 cm