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 Z is 43 cm long and Line A 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 4 cm by 3 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
= 24 ÷ 3
= 8 cm
Breadth of two squares
= Breadth x 2
= 8 x 2
= 16 cm
Length of the cuboid
= (43 - 16) ÷ 2
= 13.5 cm
Volume of the cuboid
= 13.5 x 8 x 8
= 864 cm
3 (b)
Volume of one box of candy canes
= 4 x 3 x 1
= 12 cm
3 Volume of space occupied
= 864 x 70%
= 604.8 cm
3 Estimated number of small boxes
= 604.8 ÷ 12
≈ 50.4
Minimum number of small boxes to occupy more than 70% of the carton
= 50 + 1
= 51
Answer(s): (a) 864 cm
3; (b) 51