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 J is 44 cm long and Line K is 24 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of caramel apples. Each box of caramel apples is 3 cm by 2 cm by 2 cm. If all these small boxes of caramel apples in the carton occupy more than 60% of the carton's volume, what is the minimum number of small boxes of caramel apples 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
= (44 - 16) ÷ 2
= 14 cm
Volume of the cuboid
= 14 x 8 x 8
= 896 cm
3 (b)
Volume of one box of caramel apples
= 3 x 2 x 2
= 12 cm
3 Volume of space occupied
= 896 x 60%
= 537.6 cm
3 Estimated number of small boxes
= 537.6 ÷ 12
≈ 44.8
Minimum number of small boxes to occupy more than 60% of the carton
= 44 + 1
= 45
Answer(s): (a) 896 cm
3; (b) 45