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 N is 36 cm long and Line P 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 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
= 15 ÷ 3
= 5 cm
Breadth of two squares
= Breadth x 2
= 5 x 2
= 10 cm
Length of the cuboid
= (36 - 10) ÷ 2
= 13 cm
Volume of the cuboid
= 13 x 5 x 5
= 325 cm
3 (b)
Volume of one box of chocolate bars
= 4 x 3 x 1
= 12 cm
3 Volume of space occupied
= 325 x 60%
= 195 cm
3 Estimated number of small boxes
= 195 ÷ 12
≈ 16.3
Minimum number of small boxes to occupy more than 60% of the carton
= 16 + 1
= 17
Answer(s): (a) 325 cm
3; (b) 17