The figure shows a wooden cuboid that measures 118 cm by 41 cm by 41 cm.
- Find the maximum number of 4-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
= 118 ÷ 4
= 29 r 2
Breath = Height
Number of cubes along the breadth or height
= 41 ÷ 4
= 10 r 1
Maximum number of 4 cm cubes
= 29 x 10 x 10
= 2900
(b)
Area of the 2 squares
= 2 x 41 x 41
= 3362 cm
2 Area of the top and bottom bases
= 2 x 118 x 41
= 9676 cm
2 Area of 1 L-shaped side
= 118 x 1 + (41 - 1) x 2
= 118 + 80
= 198 cm
2Area of 2 L-shaped sides
= 2 x 198
= 396 cm
2 Total surface area
= 9676 + 3362 + 396
= 13434 cm
2 Answer(s): (a) 2900; (b) 13434 cm
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