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 E is 34 cm long and Line F 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 4 cm by 2 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
= 18 ÷ 3
= 6 cm
Breadth of two squares
= Breadth x 2
= 6 x 2
= 12 cm
Length of the cuboid
= (34 - 12) ÷ 2
= 11 cm
Volume of the cuboid
= 11 x 6 x 6
= 396 cm
3 (b)
Volume of one box of sweets
= 4 x 2 x 1
= 8 cm
3 Volume of space occupied
= 396 x 50%
= 198 cm
3 Estimated number of small boxes
= 198 ÷ 8
≈ 24.8
Minimum number of small boxes to occupy more than 50% of the carton
= 24 + 1
= 25
Answer(s): (a) 396 cm
3; (b) 25