Question

A prism has a base as a right angled triangle with base 6 cm and altitude 8 cm. It is filled with water to a certain height. If a solid cube of side 6 cm is immersed in the prism, then find the height by which the water level will rise.

Answer 1

Let the initial height of water = $h_1$

Let the final height after immersing the cube be $=h_2$

Area of the triangular base (A) $=\frac{1}{2}\times 6\times 8=24c{m}^2$

Initial volume $=A{h}_1=24h_1$

Final volume $=A{h}_2=24h_2$

Change in volume of prism occupied = Volume of cube added

$24h_2-24h_1=(6{)}^3$

$24(h_2-h_1)=6\times 6\times 6$

$h_2-h_1=\frac{6\times 6\times 6}{24}$

$h_2-h_1=9cm$

So, water level rises by 9 cm.