The figure shows a wooden cuboid that measures 127 cm by 10 cm by 10 cm.
- Find the maximum number of 9-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
= 127 ÷ 9
= 14 r 1
Breath = Height
Number of cubes along the breadth or height
= 10 ÷ 9
= 1 r 1
Maximum number of 9 cm cubes
= 14 x 1 x 1
= 14
(b)
Area of the 2 squares
= 2 x 10 x 10
= 200 cm
2 Area of the top and bottom bases
= 2 x 127 x 10
= 2540 cm
2 Area of 1 L-shaped side
= 127 x 1 + (10 - 1) x 1
= 127 + 9
= 136 cm
2Area of 2 L-shaped sides
= 2 x 136
= 272 cm
2 Total surface area
= 2540 + 200 + 272
= 3012 cm
2 Answer(s): (a) 14; (b) 3012 cm
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