David has some large cubes and 18 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 large cubes does David have?
2. The volume of the tank is 129024 cm³. If the small cubes took up ⁴₇ of the tank, what is the length of the edge of one large 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 18 small cubes.

Number of small cubes that can stack vertically 
= 18 ÷ 6
= 3

Height of the tank
= 3 x 2 u
= 6 u

Number of large cubes that can stack vertically
= 6 u ÷ 3 u
= 2

Total number of large cubes used
= 2 x 2
= 4

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

Volume of the tank taken by the large cubes
= ³₇ x 129024
= 55296 cm³
= 55296 ÷ 4
= 13824 cm³

Length of one large cube
= ³√13824
= 24 cm

Answer(s): (a) 4; (b) 24 cm