PSLE Abi 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 = 51 --- (1)
Tower B:
3 h + 2 b = 84 --- (2)
Make b the same.
(1)
x2 = (3)
4 h + 2 b = 102 --- (3)
(3) - (2)
(4 h + 2 b) - (3 h + 2 b) = 102 - 84
4 h - 3 h = 18
1 h = 18 cm
(b)
Substitute 1 h = 18 into (1).
2 h + 1 b = 51
2 x 18 + 1 b = 51
36 + 1 b = 51
1 b = 51 - 36 = 15
Volume of the cuboid
= 15 x 15 x 18
= 4050 cm
3 Answer(s): (a) 18 cm; (b) 4050 cm
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