PSLE Tommy wanted to build a set of steps with 5-cm cubes. The figures show how he built the steps from a height of 10 cm to 15 cm to 20 cm. If Tommy continued building the steps in this way, what would be the height of the set of steps that had 480 cubes? Express your answer in cm.
Cubes needed for 10-cm steps = 4 x 3 = 4 x (1 + 2) = 12 cubes
Cubes needed for 15-cm steps = 4 x 6 = 4 x (1 + 2 + 3) = 24 cubes
Cubes needed for 20-cm steps = 4 x 10 = 4 x (1 + 2 + 3 + 4) = 40 cubes
Formula:
Number of cubes needed for the set of steps
= 4 x (1 + 2 + 3 + ... + Height)
= 4 x
(Height) x (Height + 1)2
4 x (Height) x (Height + 1)2 = 480
Height x (Height + 1)2 = 480 ÷ 4
Height x (Height + 1)2 = 120
Height x (Height + 1) = 120 x 2
Height x (Height + 1) = 240
15 x 16 = 240
Number of cubes needed for the height of the set of steps that had 480 cubes = 15
Height of the set of steps that had 480 cubes
= 15 x 5
= 75 cm
Answer(s): 75 cm