The figure shows a metallic cuboid that measures 115 m by 39 m by 39 m.
- Find the maximum number of 4-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
= 115 ÷ 4
= 28 r 3
Breath = Height
Number of cubes along the breadth or height
= 39 ÷ 4
= 9 r 3
Maximum number of 4 m cubes
= 28 x 9 x 9
= 2268
(b)
Area of the 2 squares
= 2 x 39 x 39
= 3042 m
2 Area of the top and bottom bases
= 2 x 115 x 39
= 8970 m
2 Area of 1 L-shaped side
= 115 x 3 + (39 - 3) x 3
= 345 + 108
= 453 m
2Area of 2 L-shaped sides
= 2 x 453
= 906 m
2 Total surface area
= 8970 + 3042 + 906
= 12918 m
2 Answer(s): (a) 2268; (b) 12918 m
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