PSLE Joelle 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 = 55 --- (1)
Tower B:
3 h + 2 b = 90 --- (2)
Make b the same.
(1)
x2 = (3)
4 h + 2 b = 110 --- (3)
(3) - (2)
(4 h + 2 b) - (3 h + 2 b) = 110 - 90
4 h - 3 h = 20
1 h = 20 cm
(b)
Substitute 1 h = 20 into (1).
2 h + 1 b = 55
2 x 20 + 1 b = 55
40 + 1 b = 55
1 b = 55 - 40 = 15
Volume of the cuboid
= 15 x 15 x 20
= 4500 cm
3 Answer(s): (a) 20 cm; (b) 4500 cm
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