The figure shows a plastic cuboid that measures 123 cm by 41 cm by 41 cm.
- Find the maximum number of 8-cm cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 123 ÷ 8
= 15 r 3
Breath = Height
Number of cubes along the breadth or height
= 41 ÷ 8
= 5 r 1
Maximum number of 8 cm cubes
= 15 x 5 x 5
= 375
(b)
Area of the 2 squares
= 2 x 41 x 41
= 3362 cm
2 Area of the top and bottom bases
= 2 x 123 x 41
= 10086 cm
2 Area of 1 L-shaped side
= 123 x 1 + (41 - 1) x 3
= 123 + 120
= 243 cm
2Area of 2 L-shaped sides
= 2 x 243
= 486 cm
2 Total surface area
= 10086 + 3362 + 486
= 13934 cm
2 Answer(s): (a) 375; (b) 13934 cm
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