The figure shows a plastic cuboid that measures 137 m by 23 m by 23 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
= 137 ÷ 4
= 34 r 1
Breath = Height
Number of cubes along the breadth or height
= 23 ÷ 4
= 5 r 3
Maximum number of 4 m cubes
= 34 x 5 x 5
= 850
(b)
Area of the 2 squares
= 2 x 23 x 23
= 1058 m
2 Area of the top and bottom bases
= 2 x 137 x 23
= 6302 m
2 Area of 1 L-shaped side
= 137 x 3 + (23 - 3) x 1
= 411 + 20
= 431 m
2Area of 2 L-shaped sides
= 2 x 431
= 862 m
2 Total surface area
= 6302 + 1058 + 862
= 8222 m
2 Answer(s): (a) 850; (b) 8222 m
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