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 U is 50 cm long and Line V is 15 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of sweets. Each box of sweets is 3 cm by 2 cm by 2 cm. If all these small boxes of sweets in the carton occupy more than 75% of the carton's volume, what is the minimum number of small boxes of sweets 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 sweets
= 3 x 2 x 2
= 12 cm
3 Volume of space occupied
= 500 x 75%
= 375 cm
3 Estimated number of small boxes
= 375 ÷ 12
≈ 31.3
Minimum number of small boxes to occupy more than 75% of the carton
= 31 + 1
= 32
Answer(s): (a) 500 cm
3; (b) 32