The figure shows a plastic cuboid that measures 113 m by 36 m by 36 m.
- Find the maximum number of 5-m cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 113 ÷ 5
= 22 r 3
Breath = Height
Number of cubes along the breadth or height
= 36 ÷ 5
= 7 r 1
Maximum number of 5 m cubes
= 22 x 7 x 7
= 1078
(b)
Area of the 2 squares
= 2 x 36 x 36
= 2592 m
2 Area of the top and bottom bases
= 2 x 113 x 36
= 8136 m
2 Area of 1 L-shaped side
= 113 x 1 + (36 - 1) x 3
= 113 + 105
= 218 m
2Area of 2 L-shaped sides
= 2 x 218
= 436 m
2 Total surface area
= 8136 + 2592 + 436
= 11164 m
2 Answer(s): (a) 1078; (b) 11164 m
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