The figure shows a wooden cuboid that measures 110 m by 45 m by 45 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
= 110 ÷ 8
= 13 r 6
Breath = Height
Number of cubes along the breadth or height
= 45 ÷ 8
= 5 r 5
Maximum number of 8 m cubes
= 13 x 5 x 5
= 325
(b)
Area of the 2 squares
= 2 x 45 x 45
= 4050 m
2 Area of the top and bottom bases
= 2 x 110 x 45
= 9900 m
2 Area of 1 L-shaped side
= 110 x 5 + (45 - 5) x 6
= 550 + 240
= 790 m
2Area of 2 L-shaped sides
= 2 x 790
= 1580 m
2 Total surface area
= 9900 + 4050 + 1580
= 15530 m
2 Answer(s): (a) 325; (b) 15530 m
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