Ryan has 4 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.
- How many small cubes does Ryan have?
- The volume of the tank is 6804 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 4 large cubes.
Number of large cubes that can stack vertically
= 4 ÷ 2
= 2
Height of the tank
= 2 x 3 u
= 6 u
Number of small cubes that can stack vertically
= 6 u ÷ 2 u
= 3
Total number of small cubes used
= 3 x 6
= 18
(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 6804
= 3888 cm
3
Volume of one small cube
= 3888 ÷ 18
= 216 cm
3 Length of one small cube
= ³√216
= 6 cm
Answer(s): (a) 18; (b) 6 cm