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 W is 44 cm long and Line X 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
= (44 - 16) ÷ 2
= 14 cm
Volume of the cuboid
= 14 x 8 x 8
= 896 cm
3 (b)
Volume of one box of candy canes
= 3 x 2 x 1
= 6 cm
3 Volume of space occupied
= 896 x 50%
= 448 cm
3 Estimated number of small boxes
= 448 ÷ 6
≈ 74.7
Minimum number of small boxes to occupy more than 50% of the carton
= 74 + 1
= 75
Answer(s): (a) 896 cm
3; (b) 75