The figure shows a rubber cuboid that measures 106 m by 23 m by 23 m.
- Find the maximum number of 9-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
= 106 ÷ 9
= 11 r 7
Breath = Height
Number of cubes along the breadth or height
= 23 ÷ 9
= 2 r 5
Maximum number of 9 m cubes
= 11 x 2 x 2
= 44
(b)
Area of the 2 squares
= 2 x 23 x 23
= 1058 m
2 Area of the top and bottom bases
= 2 x 106 x 23
= 4876 m
2 Area of 1 L-shaped side
= 106 x 5 + (23 - 5) x 7
= 530 + 126
= 656 m
2Area of 2 L-shaped sides
= 2 x 656
= 1312 m
2 Total surface area
= 4876 + 1058 + 1312
= 7246 m
2 Answer(s): (a) 44; (b) 7246 m
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