The figure shows a wooden cuboid that measures 145 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
= 145 ÷ 4
= 36 r 1
Breath = Height
Number of cubes along the breadth or height
= 19 ÷ 4
= 4 r 3
Maximum number of 4 cm cubes
= 36 x 4 x 4
= 576
(b)
Area of the 2 squares
= 2 x 19 x 19
= 722 cm
2 Area of the top and bottom bases
= 2 x 145 x 19
= 5510 cm
2 Area of 1 L-shaped side
= 145 x 3 + (19 - 3) x 1
= 435 + 16
= 451 cm
2Area of 2 L-shaped sides
= 2 x 451
= 902 cm
2 Total surface area
= 5510 + 722 + 902
= 7134 cm
2 Answer(s): (a) 576; (b) 7134 cm
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