The figure shows a wooden cuboid that measures 128 cm by 47 cm by 47 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
= 128 ÷ 6
= 21 r 2
Breath = Height
Number of cubes along the breadth or height
= 47 ÷ 6
= 7 r 5
Maximum number of 6 cm cubes
= 21 x 7 x 7
= 1029
(b)
Area of the 2 squares
= 2 x 47 x 47
= 4418 cm
2 Area of the top and bottom bases
= 2 x 128 x 47
= 12032 cm
2 Area of 1 L-shaped side
= 128 x 5 + (47 - 5) x 2
= 640 + 84
= 724 cm
2Area of 2 L-shaped sides
= 2 x 724
= 1448 cm
2 Total surface area
= 12032 + 4418 + 1448
= 17898 cm
2 Answer(s): (a) 1029; (b) 17898 cm
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