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 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 3 cm by 2 cm. If all these small boxes of chocolate bars in the carton occupy more than 75% 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
= (42 - 10) ÷ 2
= 16 cm
Volume of the cuboid
= 16 x 5 x 5
= 400 cm
3 (b)
Volume of one box of chocolate bars
= 4 x 3 x 2
= 24 cm
3 Volume of space occupied
= 400 x 75%
= 300 cm
3 Estimated number of small boxes
= 300 ÷ 24
≈ 12.5
Minimum number of small boxes to occupy more than 75% of the carton
= 12 + 1
= 13
Answer(s): (a) 400 cm
3; (b) 13