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 E is 39 cm long and Line F is 24 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of lollipops. Each box of lollipops is 3 cm by 3 cm by 1 cm. If all these small boxes of lollipops in the carton occupy more than 60% of the carton's volume, what is the minimum number of small boxes of lollipops 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
= (39 - 16) ÷ 2
= 11.5 cm
Volume of the cuboid
= 11.5 x 8 x 8
= 736 cm
3 (b)
Volume of one box of lollipops
= 3 x 3 x 1
= 9 cm
3 Volume of space occupied
= 736 x 60%
= 441.6 cm
3 Estimated number of small boxes
= 441.6 ÷ 9
≈ 49.1
Minimum number of small boxes to occupy more than 60% of the carton
= 49 + 1
= 50
Answer(s): (a) 736 cm
3; (b) 50