The figure shows a wooden cuboid that measures 122 cm by 43 cm by 43 cm.
- Find the maximum number of 5-cm 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
= 122 ÷ 5
= 24 r 2
Breath = Height
Number of cubes along the breadth or height
= 43 ÷ 5
= 8 r 3
Maximum number of 5 cm cubes
= 24 x 8 x 8
= 1536
(b)
Area of the 2 squares
= 2 x 43 x 43
= 3698 cm
2 Area of the top and bottom bases
= 2 x 122 x 43
= 10492 cm
2 Area of 1 L-shaped side
= 122 x 3 + (43 - 3) x 2
= 366 + 80
= 446 cm
2Area of 2 L-shaped sides
= 2 x 446
= 892 cm
2 Total surface area
= 10492 + 3698 + 892
= 15082 cm
2 Answer(s): (a) 1536; (b) 15082 cm
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