The figure shows a metallic cuboid that measures 116 m by 35 m by 35 m.
- Find the maximum number of 3-m cubes that can be cut from the metallic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 116 ÷ 3
= 38 r 2
Breath = Height
Number of cubes along the breadth or height
= 35 ÷ 3
= 11 r 2
Maximum number of 3 m cubes
= 38 x 11 x 11
= 4598
(b)
Area of the 2 squares
= 2 x 35 x 35
= 2450 m
2 Area of the top and bottom bases
= 2 x 116 x 35
= 8120 m
2 Area of 1 L-shaped side
= 116 x 2 + (35 - 2) x 2
= 232 + 66
= 298 m
2Area of 2 L-shaped sides
= 2 x 298
= 596 m
2 Total surface area
= 8120 + 2450 + 596
= 11166 m
2 Answer(s): (a) 4598; (b) 11166 m
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