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 21 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of sweets. Each box of sweets is 3 cm by 3 cm by 1 cm. If all these small boxes of sweets in the carton occupy more than 50% of the carton's volume, what is the minimum number of small boxes of sweets in the carton?
(a)
Breadth of the cuboid
= 21 ÷ 3
= 7 cm
Breadth of two squares
= Breadth x 2
= 7 x 2
= 14 cm
Length of the cuboid
= (36 - 14) ÷ 2
= 11 cm
Volume of the cuboid
= 11 x 7 x 7
= 539 cm
3 (b)
Volume of one box of sweets
= 3 x 3 x 1
= 9 cm
3 Volume of space occupied
= 539 x 50%
= 269.5 cm
3 Estimated number of small boxes
= 269.5 ÷ 9
≈ 29.9
Minimum number of small boxes to occupy more than 50% of the carton
= 29 + 1
= 30
Answer(s): (a) 539 cm
3; (b) 30