The figure shows a wooden cuboid that measures 115 m by 49 m by 49 m.
- Find the maximum number of 8-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
= 115 ÷ 8
= 14 r 3
Breath = Height
Number of cubes along the breadth or height
= 49 ÷ 8
= 6 r 1
Maximum number of 8 m cubes
= 14 x 6 x 6
= 504
(b)
Area of the 2 squares
= 2 x 49 x 49
= 4802 m
2 Area of the top and bottom bases
= 2 x 115 x 49
= 11270 m
2 Area of 1 L-shaped side
= 115 x 1 + (49 - 1) x 3
= 115 + 144
= 259 m
2Area of 2 L-shaped sides
= 2 x 259
= 518 m
2 Total surface area
= 11270 + 4802 + 518
= 16590 m
2 Answer(s): (a) 504; (b) 16590 m
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