The figure shows a wooden cuboid that measures 148 cm by 40 cm by 40 cm.
- Find the maximum number of 6-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
= 148 ÷ 6
= 24 r 4
Breath = Height
Number of cubes along the breadth or height
= 40 ÷ 6
= 6 r 4
Maximum number of 6 cm cubes
= 24 x 6 x 6
= 864
(b)
Area of the 2 squares
= 2 x 40 x 40
= 3200 cm
2 Area of the top and bottom bases
= 2 x 148 x 40
= 11840 cm
2 Area of 1 L-shaped side
= 148 x 4 + (40 - 4) x 4
= 592 + 144
= 736 cm
2Area of 2 L-shaped sides
= 2 x 736
= 1472 cm
2 Total surface area
= 11840 + 3200 + 1472
= 16512 cm
2 Answer(s): (a) 864; (b) 16512 cm
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