The figure shows a wooden cuboid that measures 111 m by 45 m by 45 m.
- Find the maximum number of 6-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
= 111 ÷ 6
= 18 r 3
Breath = Height
Number of cubes along the breadth or height
= 45 ÷ 6
= 7 r 3
Maximum number of 6 m cubes
= 18 x 7 x 7
= 882
(b)
Area of the 2 squares
= 2 x 45 x 45
= 4050 m
2 Area of the top and bottom bases
= 2 x 111 x 45
= 9990 m
2 Area of 1 L-shaped side
= 111 x 3 + (45 - 3) x 3
= 333 + 126
= 459 m
2Area of 2 L-shaped sides
= 2 x 459
= 918 m
2 Total surface area
= 9990 + 4050 + 918
= 14958 m
2 Answer(s): (a) 882; (b) 14958 m
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