The figure shows a metallic cuboid that measures 126 m by 42 m by 42 m.
- Find the maximum number of 8-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
= 126 ÷ 8
= 15 r 6
Breath = Height
Number of cubes along the breadth or height
= 42 ÷ 8
= 5 r 2
Maximum number of 8 m cubes
= 15 x 5 x 5
= 375
(b)
Area of the 2 squares
= 2 x 42 x 42
= 3528 m
2 Area of the top and bottom bases
= 2 x 126 x 42
= 10584 m
2 Area of 1 L-shaped side
= 126 x 2 + (42 - 2) x 6
= 252 + 240
= 492 m
2Area of 2 L-shaped sides
= 2 x 492
= 984 m
2 Total surface area
= 10584 + 3528 + 984
= 15096 m
2 Answer(s): (a) 375; (b) 15096 m
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