The figure shows a wooden cuboid that measures 136 cm by 46 cm by 46 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
= 136 ÷ 6
= 22 r 4
Breath = Height
Number of cubes along the breadth or height
= 46 ÷ 6
= 7 r 4
Maximum number of 6 cm cubes
= 22 x 7 x 7
= 1078
(b)
Area of the 2 squares
= 2 x 46 x 46
= 4232 cm
2 Area of the top and bottom bases
= 2 x 136 x 46
= 12512 cm
2 Area of 1 L-shaped side
= 136 x 4 + (46 - 4) x 4
= 544 + 168
= 712 cm
2Area of 2 L-shaped sides
= 2 x 712
= 1424 cm
2 Total surface area
= 12512 + 4232 + 1424
= 18168 cm
2 Answer(s): (a) 1078; (b) 18168 cm
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