The figure shows a wooden cuboid that measures 113 cm by 19 cm by 19 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
= 113 ÷ 4
= 28 r 1
Breath = Height
Number of cubes along the breadth or height
= 19 ÷ 4
= 4 r 3
Maximum number of 4 cm cubes
= 28 x 4 x 4
= 448
(b)
Area of the 2 squares
= 2 x 19 x 19
= 722 cm
2 Area of the top and bottom bases
= 2 x 113 x 19
= 4294 cm
2 Area of 1 L-shaped side
= 113 x 3 + (19 - 3) x 1
= 339 + 16
= 355 cm
2Area of 2 L-shaped sides
= 2 x 355
= 710 cm
2 Total surface area
= 4294 + 722 + 710
= 5726 cm
2 Answer(s): (a) 448; (b) 5726 cm
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