The figure shows a rubber cuboid that measures 107 m by 27 m by 27 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
= 107 ÷ 7
= 15 r 2
Breath = Height
Number of cubes along the breadth or height
= 27 ÷ 7
= 3 r 6
Maximum number of 7 m cubes
= 15 x 3 x 3
= 135
(b)
Area of the 2 squares
= 2 x 27 x 27
= 1458 m
2 Area of the top and bottom bases
= 2 x 107 x 27
= 5778 m
2 Area of 1 L-shaped side
= 107 x 6 + (27 - 6) x 2
= 642 + 42
= 684 m
2Area of 2 L-shaped sides
= 2 x 684
= 1368 m
2 Total surface area
= 5778 + 1458 + 1368
= 8604 m
2 Answer(s): (a) 135; (b) 8604 m
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