Blocks in a box

Level 2

A cubic box of length $2\text{ cm}$ has water in it to a depth of $0.61\text{ cm}.$

Four identical steel cubes of length $1\text{ cm}$ are placed in the box, as shown, displacing some of the water.

What is the new depth of the water in $\text{cm}?$

1 solution

Jeremy Galvagni
Apr 7, 2018

The Volume of water is $V=.61cm*2cm*2cm=2.44cm^{3}$

After adding the cubes, the water will completely fill the lower cavity which has volume $1^{3}=1cm^{3}$

The additional $2.44-1=1.44cm^{3}$ will rise as an irregular cylinder with base $3cm^{2}$

and height $1.44/3=.48cm$

The total height is therefore $1 + .48 = \boxed{1.48}cm$