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 F is 32 cm long and Line G 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 2 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
= (32 - 12) ÷ 2
= 10 cm
Volume of the cuboid
= 10 x 6 x 6
= 360 cm
3 (b)
Volume of one box of sweets
= 4 x 2 x 2
= 16 cm
3 Volume of space occupied
= 360 x 50%
= 180 cm
3 Estimated number of small boxes
= 180 ÷ 16
≈ 11.3
Minimum number of small boxes to occupy more than 50% of the carton
= 11 + 1
= 12
Answer(s): (a) 360 cm
3; (b) 12