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 R is 32 cm long and Line S is 15 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 3 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
= 15 ÷ 3
= 5 cm
Breadth of two squares
= Breadth x 2
= 5 x 2
= 10 cm
Length of the cuboid
= (32 - 10) ÷ 2
= 11 cm
Volume of the cuboid
= 11 x 5 x 5
= 275 cm
3 (b)
Volume of one box of sweets
= 4 x 3 x 2
= 24 cm
3 Volume of space occupied
= 275 x 50%
= 137.5 cm
3 Estimated number of small boxes
= 137.5 ÷ 24
≈ 5.7
Minimum number of small boxes to occupy more than 50% of the carton
= 5 + 1
= 6
Answer(s): (a) 275 cm
3; (b) 6