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 P is 48 cm long and Line Q 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 3 cm by 1 cm. If all these small boxes of mini cupcakes in the carton occupy more than 50% 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
= (48 - 16) ÷ 2
= 16 cm
Volume of the cuboid
= 16 x 8 x 8
= 1024 cm
3 (b)
Volume of one box of mini cupcakes
= 4 x 3 x 1
= 12 cm
3 Volume of space occupied
= 1024 x 50%
= 512 cm
3 Estimated number of small boxes
= 512 ÷ 12
≈ 42.7
Minimum number of small boxes to occupy more than 50% of the carton
= 42 + 1
= 43
Answer(s): (a) 1024 cm
3; (b) 43