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 50 cm long and Line L is 24 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 3 cm by 2 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
= 24 ÷ 3
= 8 cm
Breadth of two squares
= Breadth x 2
= 8 x 2
= 16 cm
Length of the cuboid
= (50 - 16) ÷ 2
= 17 cm
Volume of the cuboid
= 17 x 8 x 8
= 1088 cm
3 (b)
Volume of one box of mochi balls
= 3 x 3 x 2
= 18 cm
3 Volume of space occupied
= 1088 x 50%
= 544 cm
3 Estimated number of small boxes
= 544 ÷ 18
≈ 30.2
Minimum number of small boxes to occupy more than 50% of the carton
= 30 + 1
= 31
Answer(s): (a) 1088 cm
3; (b) 31