The figure shows a wooden cuboid that measures 121 m by 37 m by 37 m.
- Find the maximum number of 5-m cubes that can be cut from the wooden cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 121 ÷ 5
= 24 r 1
Breath = Height
Number of cubes along the breadth or height
= 37 ÷ 5
= 7 r 2
Maximum number of 5 m cubes
= 24 x 7 x 7
= 1176
(b)
Area of the 2 squares
= 2 x 37 x 37
= 2738 m
2 Area of the top and bottom bases
= 2 x 121 x 37
= 8954 m
2 Area of 1 L-shaped side
= 121 x 2 + (37 - 2) x 1
= 242 + 35
= 277 m
2Area of 2 L-shaped sides
= 2 x 277
= 554 m
2 Total surface area
= 8954 + 2738 + 554
= 12246 m
2 Answer(s): (a) 1176; (b) 12246 m
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