Archie has 8 large cubes and some small cubes. He placed them in a rectangular tank. The tank was filled to the brim exactly. The diagram, not drawn to scale, shows the first layer of cubes.

1. How many small cubes does Archie have?
2. The volume of the tank is 258048 cm³. If the large cubes took up ³₇ of the tank, what is the length of the edge of one small cube?

3 small cubes or 2 large cubes can fill the breadth of the tank.

LCM of 2 and 3 is 6.

Length of a large cube = 3 u
Length of a small cube = 2 u

There are 8 large cubes.

Number of large cubes that can stack vertically 
= 8 ÷ 2
= 4

Height of the tank
= 4 x 3 u
= 12 u

Number of small cubes that can stack vertically
= 12 u ÷ 2 u
= 6

Total number of small cubes used
= 6 x 6
= 36

(b)
Fraction of the tank taken up by the small cubes
= 1 - ³₇
= ⁴₇

Volume of the tank taken by the small cubes
= ⁴₇ x 258048
= 147456 cm³
= 147456 ÷ 36
= 4096 cm³

Length of one small cube
= ³√4096
= 16 cm

Answer(s): (a) 36; (b) 16 cm