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 X is 38 cm long and Line Y is 21 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 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
= 21 ÷ 3
= 7 cm
Breadth of two squares
= Breadth x 2
= 7 x 2
= 14 cm
Length of the cuboid
= (38 - 14) ÷ 2
= 12 cm
Volume of the cuboid
= 12 x 7 x 7
= 588 cm
3 (b)
Volume of one box of mini cupcakes
= 3 x 2 x 2
= 12 cm
3 Volume of space occupied
= 588 x 70%
= 411.6 cm
3 Estimated number of small boxes
= 411.6 ÷ 12
≈ 34.3
Minimum number of small boxes to occupy more than 70% of the carton
= 34 + 1
= 35
Answer(s): (a) 588 cm
3; (b) 35