The figure shows a metallic cuboid that measures 100 m by 40 m by 40 m.
- Find the maximum number of 3-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
= 100 ÷ 3
= 33 r 1
Breath = Height
Number of cubes along the breadth or height
= 40 ÷ 3
= 13 r 1
Maximum number of 3 m cubes
= 33 x 13 x 13
= 5577
(b)
Area of the 2 squares
= 2 x 40 x 40
= 3200 m
2 Area of the top and bottom bases
= 2 x 100 x 40
= 8000 m
2 Area of 1 L-shaped side
= 100 x 1 + (40 - 1) x 1
= 100 + 39
= 139 m
2Area of 2 L-shaped sides
= 2 x 139
= 278 m
2 Total surface area
= 8000 + 3200 + 278
= 11478 m
2 Answer(s): (a) 5577; (b) 11478 m
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