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 K is 38 cm long and Line L is 15 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
= 15 ÷ 3
= 5 cm
Breadth of two squares
= Breadth x 2
= 5 x 2
= 10 cm
Length of the cuboid
= (38 - 10) ÷ 2
= 14 cm
Volume of the cuboid
= 14 x 5 x 5
= 350 cm
3 (b)
Volume of one box of mini cupcakes
= 4 x 2 x 1
= 8 cm
3 Volume of space occupied
= 350 x 70%
= 245 cm
3 Estimated number of small boxes
= 245 ÷ 8
≈ 30.6
Minimum number of small boxes to occupy more than 70% of the carton
= 30 + 1
= 31
Answer(s): (a) 350 cm
3; (b) 31