The figure shows a plastic cuboid that measures 112 m by 49 m by 49 m.
- Find the maximum number of 9-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
= 112 ÷ 9
= 12 r 4
Breath = Height
Number of cubes along the breadth or height
= 49 ÷ 9
= 5 r 4
Maximum number of 9 m cubes
= 12 x 5 x 5
= 300
(b)
Area of the 2 squares
= 2 x 49 x 49
= 4802 m
2 Area of the top and bottom bases
= 2 x 112 x 49
= 10976 m
2 Area of 1 L-shaped side
= 112 x 4 + (49 - 4) x 4
= 448 + 180
= 628 m
2Area of 2 L-shaped sides
= 2 x 628
= 1256 m
2 Total surface area
= 10976 + 4802 + 1256
= 17034 m
2 Answer(s): (a) 300; (b) 17034 m
2