The figure shows a wooden cuboid that measures 116 m by 50 m by 50 m.
- Find the maximum number of 9-m cubes that can be cut from the wooden cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 116 ÷ 9
= 12 r 8
Breath = Height
Number of cubes along the breadth or height
= 50 ÷ 9
= 5 r 5
Maximum number of 9 m cubes
= 12 x 5 x 5
= 300
(b)
Area of the 2 squares
= 2 x 50 x 50
= 5000 m
2 Area of the top and bottom bases
= 2 x 116 x 50
= 11600 m
2 Area of 1 L-shaped side
= 116 x 5 + (50 - 5) x 8
= 580 + 360
= 940 m
2Area of 2 L-shaped sides
= 2 x 940
= 1880 m
2 Total surface area
= 11600 + 5000 + 1880
= 18480 m
2 Answer(s): (a) 300; (b) 18480 m
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