The figure shows a wooden cuboid that measures 123 m by 29 m by 29 m.
- Find the maximum number of 9-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
= 123 ÷ 9
= 13 r 6
Breath = Height
Number of cubes along the breadth or height
= 29 ÷ 9
= 3 r 2
Maximum number of 9 m cubes
= 13 x 3 x 3
= 117
(b)
Area of the 2 squares
= 2 x 29 x 29
= 1682 m
2 Area of the top and bottom bases
= 2 x 123 x 29
= 7134 m
2 Area of 1 L-shaped side
= 123 x 2 + (29 - 2) x 6
= 246 + 162
= 408 m
2Area of 2 L-shaped sides
= 2 x 408
= 816 m
2 Total surface area
= 7134 + 1682 + 816
= 9632 m
2 Answer(s): (a) 117; (b) 9632 m
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