Riordan 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.
- How many large cubes does Riordan have?
- The volume of the tank is 86436 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 86436
= 37044 cm
3
Volume of one large cube
= 37044 ÷ 4
= 9261 cm
3 Length of one large cube
= ³√9261
= 21 cm
Answer(s): (a) 4; (b) 21 cm