The figure shows a metallic cuboid that measures 113 m by 33 m by 33 m.
- Find the maximum number of 8-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
= 113 ÷ 8
= 14 r 1
Breath = Height
Number of cubes along the breadth or height
= 33 ÷ 8
= 4 r 1
Maximum number of 8 m cubes
= 14 x 4 x 4
= 224
(b)
Area of the 2 squares
= 2 x 33 x 33
= 2178 m
2 Area of the top and bottom bases
= 2 x 113 x 33
= 7458 m
2 Area of 1 L-shaped side
= 113 x 1 + (33 - 1) x 1
= 113 + 32
= 145 m
2Area of 2 L-shaped sides
= 2 x 145
= 290 m
2 Total surface area
= 7458 + 2178 + 290
= 9926 m
2 Answer(s): (a) 224; (b) 9926 m
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