Peter 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.
- How many small cubes does Peter have?
- The volume of the tank is 63000 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 63000
= 36000 cm
3
Volume of one small cube
= 36000 ÷ 36
= 1000 cm
3 Length of one small cube
= ³√1000
= 10 cm
Answer(s): (a) 36; (b) 10 cm