Question

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

Answer 1

Diameter of cylindrical container = 56 cm

$\therefore Radius\left(r\right)=\frac{56}{2}$ = 28 cm

Dimensions of a rectangular solid are

= 32 cm $\times 22cm\times$ 14 cm

$\therefore$ Volume of solid = lbh

= 32 $\times 22\times 14=9856c{m}^3$

Let h be the rise in level of water, then

$\pi r^2$ h = 9856

$\Rightarrow \frac{22}{7}\times 28\times 28\times h=9856$

$\Rightarrow h=\frac{9856\times 7}{22\times 28\times 28}$ = 4 cm

$\therefore$ Height of water level = 4 cm