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 33 cm long and Line Y is 24 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of sweets. Each box of sweets is 4 cm by 2 cm by 2 cm. If all these small boxes of sweets in the carton occupy more than 75% of the carton's volume, what is the minimum number of small boxes of sweets 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
= (33 - 16) ÷ 2
= 8.5 cm
Volume of the cuboid
= 8.5 x 8 x 8
= 544 cm
3 (b)
Volume of one box of sweets
= 4 x 2 x 2
= 16 cm
3 Volume of space occupied
= 544 x 75%
= 408 cm
3 Estimated number of small boxes
= 408 ÷ 16
≈ 25.5
Minimum number of small boxes to occupy more than 75% of the carton
= 25 + 1
= 26
Answer(s): (a) 544 cm
3; (b) 26