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 42 cm long and Line S 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 4 cm by 3 cm by 2 cm. If all these small boxes of candy canes in the carton occupy more than 60% 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
= (42 - 14) ÷ 2
= 14 cm
Volume of the cuboid
= 14 x 7 x 7
= 686 cm
3 (b)
Volume of one box of candy canes
= 4 x 3 x 2
= 24 cm
3 Volume of space occupied
= 686 x 60%
= 411.6 cm
3 Estimated number of small boxes
= 411.6 ÷ 24
≈ 17.2
Minimum number of small boxes to occupy more than 60% of the carton
= 17 + 1
= 18
Answer(s): (a) 686 cm
3; (b) 18