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 B is 44 cm long and Line C 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 3 cm by 2 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
= 21 ÷ 3
= 7 cm
Breadth of two squares
= Breadth x 2
= 7 x 2
= 14 cm
Length of the cuboid
= (44 - 14) ÷ 2
= 15 cm
Volume of the cuboid
= 15 x 7 x 7
= 735 cm
3 (b)
Volume of one box of candy canes
= 3 x 3 x 2
= 18 cm
3 Volume of space occupied
= 735 x 50%
= 367.5 cm
3 Estimated number of small boxes
= 367.5 ÷ 18
≈ 20.4
Minimum number of small boxes to occupy more than 50% of the carton
= 20 + 1
= 21
Answer(s): (a) 735 cm
3; (b) 21