PSLE Tammy 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 = 37 --- (1)
Tower B:
3 h + 2 b = 60 --- (2)
Make b the same.
(1)
x2 = (3)
4 h + 2 b = 74 --- (3)
(3) - (2)
(4 h + 2 b) - (3 h + 2 b) = 74 - 60
4 h - 3 h = 14
1 h = 14 cm
(b)
Substitute 1 h = 14 into (1).
2 h + 1 b = 37
2 x 14 + 1 b = 37
28 + 1 b = 37
1 b = 37 - 28 = 9
Volume of the cuboid
= 9 x 9 x 14
= 1134 cm
3 Answer(s): (a) 14 cm; (b) 1134 cm
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