1. ## cuboids

a rectangular tank 25 m long & 20 cm wide contains water to a depth of 5cm. a metal cube of side 8cm is palced in the tank so that one face of the cube rests on the bottom of the tank. find how how many litres of water must be poured into the tank so as to just cover the cube.

2. Hello, samanta!

It sounded like a complicated problem, but a little baby-talk helped.

A rectangular tank 25 m long & 20 cm wide contains water to a depth of 5cm.
A metal cube of side 8 cm is placled on the bottom of the tank.
Find how many litres of water must be poured into the tank to just cover the cube.

The tank is 2500 cm long and 20 cm wide.
Filled to a depth of 5 cm, the volume of water is: . $2500 \times 20 \times 5 \:=\:250,\!000\text{ cm}^3$

The cube has a volume of: . $8^3 = 512\text{ cm}^3$
Adding it to the pool, the total volume is: . $250,\!1000 + 512 \:=\:250,\!512\text{ cm}^3$

To fill the pool to a depth of 8 cm requires: . $2500 \times 20 \times 8 \:=\:400,\!000\text{ cm}^3$

Hence, we need: . $400,\!000 - 250,\!512 \:=\:149,\!488\text{ cm}^3$ more.

. . And this is about $\boxed{149.5\text{ litres}}$