The figure shows a rubber cuboid that measures 117 m by 31 m by 31 m.
- Find the maximum number of 4-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
= 117 ÷ 4
= 29 r 1
Breath = Height
Number of cubes along the breadth or height
= 31 ÷ 4
= 7 r 3
Maximum number of 4 m cubes
= 29 x 7 x 7
= 1421
(b)
Area of the 2 squares
= 2 x 31 x 31
= 1922 m
2 Area of the top and bottom bases
= 2 x 117 x 31
= 7254 m
2 Area of 1 L-shaped side
= 117 x 3 + (31 - 3) x 1
= 351 + 28
= 379 m
2Area of 2 L-shaped sides
= 2 x 379
= 758 m
2 Total surface area
= 7254 + 1922 + 758
= 9934 m
2 Answer(s): (a) 1421; (b) 9934 m
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