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 C is 42 cm long and Line D is 24 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 3 cm by 1 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
= 24 ÷ 3
= 8 cm
Breadth of two squares
= Breadth x 2
= 8 x 2
= 16 cm
Length of the cuboid
= (42 - 16) ÷ 2
= 13 cm
Volume of the cuboid
= 13 x 8 x 8
= 832 cm
3 (b)
Volume of one box of chocolate bars
= 4 x 3 x 1
= 12 cm
3 Volume of space occupied
= 832 x 60%
= 499.2 cm
3 Estimated number of small boxes
= 499.2 ÷ 12
≈ 41.6
Minimum number of small boxes to occupy more than 60% of the carton
= 41 + 1
= 42
Answer(s): (a) 832 cm
3; (b) 42