The figure shows a rubber cuboid that measures 120 m by 31 m by 31 m.
- Find the maximum number of 7-m 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
= 120 ÷ 7
= 17 r 1
Breath = Height
Number of cubes along the breadth or height
= 31 ÷ 7
= 4 r 3
Maximum number of 7 m cubes
= 17 x 4 x 4
= 272
(b)
Area of the 2 squares
= 2 x 31 x 31
= 1922 m
2 Area of the top and bottom bases
= 2 x 120 x 31
= 7440 m
2 Area of 1 L-shaped side
= 120 x 3 + (31 - 3) x 1
= 360 + 28
= 388 m
2Area of 2 L-shaped sides
= 2 x 388
= 776 m
2 Total surface area
= 7440 + 1922 + 776
= 10138 m
2 Answer(s): (a) 272; (b) 10138 m
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