Question

A cylindrical container with diameter of base $56cm$ contains sufficient water to submerge a rectangular solid of iron with dimensions $(32\times 22cm\times 14cm)$. Find the rise in the level of water when the solid is completely submerged.

Answer 1

Given,

Diameter of the base of the cylindrical container $d=56cm$

Hence, radius of the base of the cylindrical container $r=\frac{56}{2}=28cm$

Dimensions of rectangular solid is $(32cm\times 22cm\times 14cm)$

We know that when a body is completely submerged in a container containing water,

the rise in the volume of water in the container is equal to the volume of the body.

Let, the water rises to a height $h$.

Hence,

$\text{Volume of water rises in cylindrical container =Volume of the rectangular solid}$

$\pi r^{2}h=32\times 22\times 14c{m}^3$

$\frac{22}{7}\times (28{)}^2\times h=9856cm$

$h=\frac{9856\times 7}{22\times 784}cm$

$h=4cm$