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 X is 48 cm long and Line Y 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 3 cm by 2 cm by 2 cm. If all these small boxes of chocolate bars in the carton occupy more than 60% 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
= (48 - 10) ÷ 2
= 19 cm
Volume of the cuboid
= 19 x 5 x 5
= 475 cm
3 (b)
Volume of one box of chocolate bars
= 3 x 2 x 2
= 12 cm
3 Volume of space occupied
= 475 x 60%
= 285 cm
3 Estimated number of small boxes
= 285 ÷ 12
≈ 23.8
Minimum number of small boxes to occupy more than 60% of the carton
= 23 + 1
= 24
Answer(s): (a) 475 cm
3; (b) 24