The figure shows a rubber cuboid that measures 112 m by 23 m by 23 m.
- Find the maximum number of 6-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
= 112 ÷ 6
= 18 r 4
Breath = Height
Number of cubes along the breadth or height
= 23 ÷ 6
= 3 r 5
Maximum number of 6 m cubes
= 18 x 3 x 3
= 162
(b)
Area of the 2 squares
= 2 x 23 x 23
= 1058 m
2 Area of the top and bottom bases
= 2 x 112 x 23
= 5152 m
2 Area of 1 L-shaped side
= 112 x 5 + (23 - 5) x 4
= 560 + 72
= 632 m
2Area of 2 L-shaped sides
= 2 x 632
= 1264 m
2 Total surface area
= 5152 + 1058 + 1264
= 7474 m
2 Answer(s): (a) 162; (b) 7474 m
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