The figure shows a plastic cuboid that measures 123 cm by 28 cm by 28 cm.
- Find the maximum number of 9-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 ÷ 9
= 13 r 6
Breath = Height
Number of cubes along the breadth or height
= 28 ÷ 9
= 3 r 1
Maximum number of 9 cm cubes
= 13 x 3 x 3
= 117
(b)
Area of the 2 squares
= 2 x 28 x 28
= 1568 cm
2 Area of the top and bottom bases
= 2 x 123 x 28
= 6888 cm
2 Area of 1 L-shaped side
= 123 x 1 + (28 - 1) x 6
= 123 + 162
= 285 cm
2Area of 2 L-shaped sides
= 2 x 285
= 570 cm
2 Total surface area
= 6888 + 1568 + 570
= 9026 cm
2 Answer(s): (a) 117; (b) 9026 cm
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