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 45 cm long and Line Q is 18 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 3 cm by 2 cm by 2 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
= 18 ÷ 3
= 6 cm
Breadth of two squares
= Breadth x 2
= 6 x 2
= 12 cm
Length of the cuboid
= (45 - 12) ÷ 2
= 16.5 cm
Volume of the cuboid
= 16.5 x 6 x 6
= 594 cm
3 (b)
Volume of one box of mini cupcakes
= 3 x 2 x 2
= 12 cm
3 Volume of space occupied
= 594 x 50%
= 297 cm
3 Estimated number of small boxes
= 297 ÷ 12
≈ 24.8
Minimum number of small boxes to occupy more than 50% of the carton
= 24 + 1
= 25
Answer(s): (a) 594 cm
3; (b) 25