Question

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

Answer 1

Diameter of the base of a cylindrical container=56cm


$\therefore$ Radius(r) = $\frac{56}{2}=28cm$
Dimensions of the rectangular solid
$=32cm\times 22cm\times 14cm$
$\therefore$ Volume of solid = $32\times 22\times 14c{m}^3=9856c{m}^3$
$\therefore$ Volume of water rose up = $9856c{m}^3$
Let h be the height of water, then
$\pi r^{2}h=9856\Rightarrow \frac{22}{7}\times 28\times 28\times h=9856\Rightarrow h=\frac{9856\times 7}{22\times 28\times 28}=4cm$