The figure shows a rubber cuboid that measures 100 cm by 46 cm by 46 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
= 100 ÷ 9
= 11 r 1
Breath = Height
Number of cubes along the breadth or height
= 46 ÷ 9
= 5 r 1
Maximum number of 9 cm cubes
= 11 x 5 x 5
= 275
(b)
Area of the 2 squares
= 2 x 46 x 46
= 4232 cm
2 Area of the top and bottom bases
= 2 x 100 x 46
= 9200 cm
2 Area of 1 L-shaped side
= 100 x 1 + (46 - 1) x 1
= 100 + 45
= 145 cm
2Area of 2 L-shaped sides
= 2 x 145
= 290 cm
2 Total surface area
= 9200 + 4232 + 290
= 13722 cm
2 Answer(s): (a) 275; (b) 13722 cm
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