The figure shows a plastic cuboid that measures 107 m by 29 m by 29 m.
- Find the maximum number of 9-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
= 107 ÷ 9
= 11 r 8
Breath = Height
Number of cubes along the breadth or height
= 29 ÷ 9
= 3 r 2
Maximum number of 9 m cubes
= 11 x 3 x 3
= 99
(b)
Area of the 2 squares
= 2 x 29 x 29
= 1682 m
2 Area of the top and bottom bases
= 2 x 107 x 29
= 6206 m
2 Area of 1 L-shaped side
= 107 x 2 + (29 - 2) x 8
= 214 + 216
= 430 m
2Area of 2 L-shaped sides
= 2 x 430
= 860 m
2 Total surface area
= 6206 + 1682 + 860
= 8748 m
2 Answer(s): (a) 99; (b) 8748 m
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