The figure shows a plastic cuboid that measures 131 m by 41 m by 41 m.
- Find the maximum number of 6-m cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 131 ÷ 6
= 21 r 5
Breath = Height
Number of cubes along the breadth or height
= 41 ÷ 6
= 6 r 5
Maximum number of 6 m cubes
= 21 x 6 x 6
= 756
(b)
Area of the 2 squares
= 2 x 41 x 41
= 3362 m
2 Area of the top and bottom bases
= 2 x 131 x 41
= 10742 m
2 Area of 1 L-shaped side
= 131 x 5 + (41 - 5) x 5
= 655 + 180
= 835 m
2Area of 2 L-shaped sides
= 2 x 835
= 1670 m
2 Total surface area
= 10742 + 3362 + 1670
= 15774 m
2 Answer(s): (a) 756; (b) 15774 m
2