The figure shows a plastic cuboid that measures 101 m by 39 m by 39 m.
- Find the maximum number of 8-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
= 101 ÷ 8
= 12 r 5
Breath = Height
Number of cubes along the breadth or height
= 39 ÷ 8
= 4 r 7
Maximum number of 8 m cubes
= 12 x 4 x 4
= 192
(b)
Area of the 2 squares
= 2 x 39 x 39
= 3042 m
2 Area of the top and bottom bases
= 2 x 101 x 39
= 7878 m
2 Area of 1 L-shaped side
= 101 x 7 + (39 - 7) x 5
= 707 + 160
= 867 m
2Area of 2 L-shaped sides
= 2 x 867
= 1734 m
2 Total surface area
= 7878 + 3042 + 1734
= 12654 m
2 Answer(s): (a) 192; (b) 12654 m
2