The figure shows a rubber cuboid that measures 141 cm by 32 cm by 32 cm.
- Find the maximum number of 9-cm cubes that can be cut from the rubber cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 141 ÷ 9
= 15 r 6
Breath = Height
Number of cubes along the breadth or height
= 32 ÷ 9
= 3 r 5
Maximum number of 9 cm cubes
= 15 x 3 x 3
= 135
(b)
Area of the 2 squares
= 2 x 32 x 32
= 2048 cm
2 Area of the top and bottom bases
= 2 x 141 x 32
= 9024 cm
2 Area of 1 L-shaped side
= 141 x 5 + (32 - 5) x 6
= 705 + 162
= 867 cm
2Area of 2 L-shaped sides
= 2 x 867
= 1734 cm
2 Total surface area
= 9024 + 2048 + 1734
= 12806 cm
2 Answer(s): (a) 135; (b) 12806 cm
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