The figure shows a plastic cuboid that measures 127 m by 41 m by 41 m.
- Find the maximum number of 4-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
= 127 ÷ 4
= 31 r 3
Breath = Height
Number of cubes along the breadth or height
= 41 ÷ 4
= 10 r 1
Maximum number of 4 m cubes
= 31 x 10 x 10
= 3100
(b)
Area of the 2 squares
= 2 x 41 x 41
= 3362 m
2 Area of the top and bottom bases
= 2 x 127 x 41
= 10414 m
2 Area of 1 L-shaped side
= 127 x 1 + (41 - 1) x 3
= 127 + 120
= 247 m
2Area of 2 L-shaped sides
= 2 x 247
= 494 m
2 Total surface area
= 10414 + 3362 + 494
= 14270 m
2 Answer(s): (a) 3100; (b) 14270 m
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