The figure shows a plastic cuboid that measures 136 m by 23 m by 23 m.
- Find the maximum number of 3-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
= 136 ÷ 3
= 45 r 1
Breath = Height
Number of cubes along the breadth or height
= 23 ÷ 3
= 7 r 2
Maximum number of 3 m cubes
= 45 x 7 x 7
= 2205
(b)
Area of the 2 squares
= 2 x 23 x 23
= 1058 m
2 Area of the top and bottom bases
= 2 x 136 x 23
= 6256 m
2 Area of 1 L-shaped side
= 136 x 2 + (23 - 2) x 1
= 272 + 21
= 293 m
2Area of 2 L-shaped sides
= 2 x 293
= 586 m
2 Total surface area
= 6256 + 1058 + 586
= 7900 m
2 Answer(s): (a) 2205; (b) 7900 m
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