The figure shows a wooden cuboid that measures 110 m by 37 m by 37 m.
- Find the maximum number of 8-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
= 110 ÷ 8
= 13 r 6
Breath = Height
Number of cubes along the breadth or height
= 37 ÷ 8
= 4 r 5
Maximum number of 8 m cubes
= 13 x 4 x 4
= 208
(b)
Area of the 2 squares
= 2 x 37 x 37
= 2738 m
2 Area of the top and bottom bases
= 2 x 110 x 37
= 8140 m
2 Area of 1 L-shaped side
= 110 x 5 + (37 - 5) x 6
= 550 + 192
= 742 m
2Area of 2 L-shaped sides
= 2 x 742
= 1484 m
2 Total surface area
= 8140 + 2738 + 1484
= 12362 m
2 Answer(s): (a) 208; (b) 12362 m
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