The figure shows a wooden cuboid that measures 131 m by 32 m by 32 m.
- Find the maximum number of 7-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
= 131 ÷ 7
= 18 r 5
Breath = Height
Number of cubes along the breadth or height
= 32 ÷ 7
= 4 r 4
Maximum number of 7 m cubes
= 18 x 4 x 4
= 288
(b)
Area of the 2 squares
= 2 x 32 x 32
= 2048 m
2 Area of the top and bottom bases
= 2 x 131 x 32
= 8384 m
2 Area of 1 L-shaped side
= 131 x 4 + (32 - 4) x 5
= 524 + 140
= 664 m
2Area of 2 L-shaped sides
= 2 x 664
= 1328 m
2 Total surface area
= 8384 + 2048 + 1328
= 11760 m
2 Answer(s): (a) 288; (b) 11760 m
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