The figure shows a wooden cuboid that measures 143 m by 45 m by 45 m.
- Find the maximum number of 7-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
= 143 ÷ 7
= 20 r 3
Breath = Height
Number of cubes along the breadth or height
= 45 ÷ 7
= 6 r 3
Maximum number of 7 m cubes
= 20 x 6 x 6
= 720
(b)
Area of the 2 squares
= 2 x 45 x 45
= 4050 m
2 Area of the top and bottom bases
= 2 x 143 x 45
= 12870 m
2 Area of 1 L-shaped side
= 143 x 3 + (45 - 3) x 3
= 429 + 126
= 555 m
2Area of 2 L-shaped sides
= 2 x 555
= 1110 m
2 Total surface area
= 12870 + 4050 + 1110
= 18030 m
2 Answer(s): (a) 720; (b) 18030 m
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