PSLE Nora had some identitical cuboids with square base and height, h. She then stacked the cuboid to form the 2 towers. The figure shows the front view and the side views of the 2 towers.
- Find h.
- Find the volume of the cuboid.
Tower A:
2 h + 1 b = 42 --- (1)
Tower B:
3 h + 2 b = 69 --- (2)
Make b the same.
(1)
x2 = (3)
4 h + 2 b = 84 --- (3)
(3) - (2)
(4 h + 2 b) - (3 h + 2 b) = 84 - 69
4 h - 3 h = 15
1 h = 15 cm
(b)
Substitute 1 h = 15 into (1).
2 h + 1 b = 42
2 x 15 + 1 b = 42
30 + 1 b = 42
1 b = 42 - 30 = 12
Volume of the cuboid
= 12 x 12 x 15
= 2160 cm
3 Answer(s): (a) 15 cm; (b) 2160 cm
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