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 49 cm long and Line P 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 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
= 24 ÷ 3
= 8 cm
Breadth of two squares
= Breadth x 2
= 8 x 2
= 16 cm
Length of the cuboid
= (49 - 16) ÷ 2
= 16.5 cm
Volume of the cuboid
= 16.5 x 8 x 8
= 1056 cm
3 (b)
Volume of one box of chocolate bars
= 3 x 2 x 2
= 12 cm
3 Volume of space occupied
= 1056 x 60%
= 633.6 cm
3 Estimated number of small boxes
= 633.6 ÷ 12
≈ 52.8
Minimum number of small boxes to occupy more than 60% of the carton
= 52 + 1
= 53
Answer(s): (a) 1056 cm
3; (b) 53