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 M is 42 cm long and Line N is 24 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of mini cupcakes. Each box of mini cupcakes is 4 cm by 2 cm by 1 cm. If all these small boxes of mini cupcakes in the carton occupy more than 70% of the carton's volume, what is the minimum number of small boxes of mini cupcakes 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
= (42 - 16) ÷ 2
= 13 cm
Volume of the cuboid
= 13 x 8 x 8
= 832 cm
3 (b)
Volume of one box of mini cupcakes
= 4 x 2 x 1
= 8 cm
3 Volume of space occupied
= 832 x 70%
= 582.4 cm
3 Estimated number of small boxes
= 582.4 ÷ 8
≈ 72.8
Minimum number of small boxes to occupy more than 70% of the carton
= 72 + 1
= 73
Answer(s): (a) 832 cm
3; (b) 73