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 35 cm long and Line P is 18 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 75% of the carton's volume, what is the minimum number of small boxes of sweets in the carton?
(a)
Breadth of the cuboid
= 18 ÷ 3
= 6 cm
Breadth of two squares
= Breadth x 2
= 6 x 2
= 12 cm
Length of the cuboid
= (35 - 12) ÷ 2
= 11.5 cm
Volume of the cuboid
= 11.5 x 6 x 6
= 414 cm
3 (b)
Volume of one box of sweets
= 3 x 3 x 1
= 9 cm
3 Volume of space occupied
= 414 x 75%
= 310.5 cm
3 Estimated number of small boxes
= 310.5 ÷ 9
≈ 34.5
Minimum number of small boxes to occupy more than 75% of the carton
= 34 + 1
= 35
Answer(s): (a) 414 cm
3; (b) 35