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 F is 50 cm long and Line G is 18 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 75% of the carton's volume, what is the minimum number of small boxes of candy canes in the carton?
(a)
Breadth of the cuboid
= 18 ÷ 3
= 6 cm
Breadth of two squares
= Breadth x 2
= 6 x 2
= 12 cm
Length of the cuboid
= (50 - 12) ÷ 2
= 19 cm
Volume of the cuboid
= 19 x 6 x 6
= 684 cm
3 (b)
Volume of one box of candy canes
= 4 x 3 x 2
= 24 cm
3 Volume of space occupied
= 684 x 75%
= 513 cm
3 Estimated number of small boxes
= 513 ÷ 24
≈ 21.4
Minimum number of small boxes to occupy more than 75% of the carton
= 21 + 1
= 22
Answer(s): (a) 684 cm
3; (b) 22