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 S is 45 cm long and Line T 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 4 cm by 3 cm by 1 cm. If all these small boxes of mochi balls in the carton occupy more than 60% 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
= (45 - 16) ÷ 2
= 14.5 cm
Volume of the cuboid
= 14.5 x 8 x 8
= 928 cm
3 (b)
Volume of one box of mochi balls
= 4 x 3 x 1
= 12 cm
3 Volume of space occupied
= 928 x 60%
= 556.8 cm
3 Estimated number of small boxes
= 556.8 ÷ 12
≈ 46.4
Minimum number of small boxes to occupy more than 60% of the carton
= 46 + 1
= 47
Answer(s): (a) 928 cm
3; (b) 47