The figure shows a plastic cuboid that measures 107 m by 40 m by 40 m.
- Find the maximum number of 7-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
= 107 ÷ 7
= 15 r 2
Breath = Height
Number of cubes along the breadth or height
= 40 ÷ 7
= 5 r 5
Maximum number of 7 m cubes
= 15 x 5 x 5
= 375
(b)
Area of the 2 squares
= 2 x 40 x 40
= 3200 m
2 Area of the top and bottom bases
= 2 x 107 x 40
= 8560 m
2 Area of 1 L-shaped side
= 107 x 5 + (40 - 5) x 2
= 535 + 70
= 605 m
2Area of 2 L-shaped sides
= 2 x 605
= 1210 m
2 Total surface area
= 8560 + 3200 + 1210
= 12970 m
2 Answer(s): (a) 375; (b) 12970 m
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