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 34 cm long and Line Q 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 4 cm by 3 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
= (34 - 14) ÷ 2
= 10 cm
Volume of the cuboid
= 10 x 7 x 7
= 490 cm
3 (b)
Volume of one box of mini cupcakes
= 4 x 3 x 2
= 24 cm
3 Volume of space occupied
= 490 x 70%
= 343 cm
3 Estimated number of small boxes
= 343 ÷ 24
≈ 14.3
Minimum number of small boxes to occupy more than 70% of the carton
= 14 + 1
= 15
Answer(s): (a) 490 cm
3; (b) 15