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 J is 50 cm long and Line K is 15 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 75% of the carton's volume, what is the minimum number of small boxes of mochi balls 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
= (50 - 10) ÷ 2
= 20 cm
Volume of the cuboid
= 20 x 5 x 5
= 500 cm
3 (b)
Volume of one box of mochi balls
= 3 x 3 x 2
= 18 cm
3 Volume of space occupied
= 500 x 75%
= 375 cm
3 Estimated number of small boxes
= 375 ÷ 18
≈ 20.8
Minimum number of small boxes to occupy more than 75% of the carton
= 20 + 1
= 21
Answer(s): (a) 500 cm
3; (b) 21