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 L is 33 cm long and Line M is 24 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of candy canes. Each box of candy canes is 3 cm by 2 cm by 1 cm. If all these small boxes of candy canes in the carton occupy more than 50% of the carton's volume, what is the minimum number of small boxes of candy canes in the carton?
(a)
Breadth of the cuboid
= 24 ÷ 3
= 8 cm
Breadth of two squares
= Breadth x 2
= 8 x 2
= 16 cm
Length of the cuboid
= (33 - 16) ÷ 2
= 8.5 cm
Volume of the cuboid
= 8.5 x 8 x 8
= 544 cm
3 (b)
Volume of one box of candy canes
= 3 x 2 x 1
= 6 cm
3 Volume of space occupied
= 544 x 50%
= 272 cm
3 Estimated number of small boxes
= 272 ÷ 6
≈ 45.3
Minimum number of small boxes to occupy more than 50% of the carton
= 45 + 1
= 46
Answer(s): (a) 544 cm
3; (b) 46