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 L is 34 cm long and Line M is 21 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of caramel apples. Each box of caramel apples is 4 cm by 3 cm by 1 cm. If all these small boxes of caramel apples in the carton occupy more than 75% of the carton's volume, what is the minimum number of small boxes of caramel apples in the carton?
(a)
Breadth of the cuboid
= 21 ÷ 3
= 7 cm
Breadth of two squares
= Breadth x 2
= 7 x 2
= 14 cm
Length of the cuboid
= (34 - 14) ÷ 2
= 10 cm
Volume of the cuboid
= 10 x 7 x 7
= 490 cm
3 (b)
Volume of one box of caramel apples
= 4 x 3 x 1
= 12 cm
3 Volume of space occupied
= 490 x 75%
= 367.5 cm
3 Estimated number of small boxes
= 367.5 ÷ 12
≈ 30.6
Minimum number of small boxes to occupy more than 75% of the carton
= 30 + 1
= 31
Answer(s): (a) 490 cm
3; (b) 31