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 R is 49 cm long and Line S is 24 cm long.
- Find the volume of the solid.
- This solid is a cardboard carton containing small boxes of mini cupcakes. Each box of mini cupcakes is 4 cm by 2 cm by 2 cm. If all these small boxes of mini cupcakes in the carton occupy more than 70% of the carton's volume, what is the minimum number of small boxes of mini cupcakes 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
= (49 - 16) ÷ 2
= 16.5 cm
Volume of the cuboid
= 16.5 x 8 x 8
= 1056 cm
3 (b)
Volume of one box of mini cupcakes
= 4 x 2 x 2
= 16 cm
3 Volume of space occupied
= 1056 x 70%
= 739.2 cm
3 Estimated number of small boxes
= 739.2 ÷ 16
≈ 46.2
Minimum number of small boxes to occupy more than 70% of the carton
= 46 + 1
= 47
Answer(s): (a) 1056 cm
3; (b) 47