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 41 cm long and Line L is 18 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of mochi balls. Each box of mochi balls is 3 cm by 2 cm by 1 cm. If all these small boxes of mochi balls in the carton occupy more than 50% of the carton's volume, what is the minimum number of small boxes of mochi balls 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
= (41 - 12) ÷ 2
= 14.5 cm
Volume of the cuboid
= 14.5 x 6 x 6
= 522 cm
3 (b)
Volume of one box of mochi balls
= 3 x 2 x 1
= 6 cm
3 Volume of space occupied
= 522 x 50%
= 261 cm
3 Estimated number of small boxes
= 261 ÷ 6
≈ 43.5
Minimum number of small boxes to occupy more than 50% of the carton
= 43 + 1
= 44
Answer(s): (a) 522 cm
3; (b) 44