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 V is 32 cm long and Line W is 21 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 70% of the carton's volume, what is the minimum number of small boxes of candy canes in the carton?
(a)
Breadth of the cuboid
= 21 ÷ 3
= 7 cm
Breadth of two squares
= Breadth x 2
= 7 x 2
= 14 cm
Length of the cuboid
= (32 - 14) ÷ 2
= 9 cm
Volume of the cuboid
= 9 x 7 x 7
= 441 cm
3 (b)
Volume of one box of candy canes
= 3 x 2 x 1
= 6 cm
3 Volume of space occupied
= 441 x 70%
= 308.7 cm
3 Estimated number of small boxes
= 308.7 ÷ 6
≈ 51.5
Minimum number of small boxes to occupy more than 70% of the carton
= 51 + 1
= 52
Answer(s): (a) 441 cm
3; (b) 52