The figure shows a metallic cuboid that measures 110 m by 37 m by 37 m.
- Find the maximum number of 6-m cubes that can be cut from the metallic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 110 ÷ 6
= 18 r 2
Breath = Height
Number of cubes along the breadth or height
= 37 ÷ 6
= 6 r 1
Maximum number of 6 m cubes
= 18 x 6 x 6
= 648
(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 1 + (37 - 1) x 2
= 110 + 72
= 182 m
2Area of 2 L-shaped sides
= 2 x 182
= 364 m
2 Total surface area
= 8140 + 2738 + 364
= 11242 m
2 Answer(s): (a) 648; (b) 11242 m
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