The figure is not drawn to scale. It shows the net of a solid. It is made up of 4 identical rectangles and 2 identical squares. Line B is 34 cm long and Line C is 15 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of chocolate bars. Each box of chocolate bars is 4 cm by 2 cm by 2 cm. If all these small boxes of chocolate bars in the carton occupy more than 50% of the carton's volume, what is the minimum number of small boxes of chocolate bars in the carton?
(a)
Breadth of the cuboid
= 15 ÷ 3
= 5 cm
Breadth of two squares
= Breadth x 2
= 5 x 2
= 10 cm
Length of the cuboid
= (34 - 10) ÷ 2
= 12 cm
Volume of the cuboid
= 12 x 5 x 5
= 300 cm
3 (b)
Volume of one box of chocolate bars
= 4 x 2 x 2
= 16 cm
3 Volume of space occupied
= 300 x 50%
= 150 cm
3 Estimated number of small boxes
= 150 ÷ 16
≈ 9.4
Minimum number of small boxes to occupy more than 50% of the carton
= 9 + 1
= 10
Answer(s): (a) 300 cm
3; (b) 10