The figure shows a wooden cuboid that measures 123 cm by 22 cm by 22 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
= 123 ÷ 6
= 20 r 3
Breath = Height
Number of cubes along the breadth or height
= 22 ÷ 6
= 3 r 4
Maximum number of 6 cm cubes
= 20 x 3 x 3
= 180
(b)
Area of the 2 squares
= 2 x 22 x 22
= 968 cm
2 Area of the top and bottom bases
= 2 x 123 x 22
= 5412 cm
2 Area of 1 L-shaped side
= 123 x 4 + (22 - 4) x 3
= 492 + 54
= 546 cm
2Area of 2 L-shaped sides
= 2 x 546
= 1092 cm
2 Total surface area
= 5412 + 968 + 1092
= 7472 cm
2 Answer(s): (a) 180; (b) 7472 cm
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