The figure shows a wooden cuboid that measures 106 cm by 17 cm by 17 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
= 106 ÷ 4
= 26 r 2
Breath = Height
Number of cubes along the breadth or height
= 17 ÷ 4
= 4 r 1
Maximum number of 4 cm cubes
= 26 x 4 x 4
= 416
(b)
Area of the 2 squares
= 2 x 17 x 17
= 578 cm
2 Area of the top and bottom bases
= 2 x 106 x 17
= 3604 cm
2 Area of 1 L-shaped side
= 106 x 1 + (17 - 1) x 2
= 106 + 32
= 138 cm
2Area of 2 L-shaped sides
= 2 x 138
= 276 cm
2 Total surface area
= 3604 + 578 + 276
= 4458 cm
2 Answer(s): (a) 416; (b) 4458 cm
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