The figure shows a metallic cuboid that measures 137 m by 50 m by 50 m.
- Find the maximum number of 7-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
= 137 ÷ 7
= 19 r 4
Breath = Height
Number of cubes along the breadth or height
= 50 ÷ 7
= 7 r 1
Maximum number of 7 m cubes
= 19 x 7 x 7
= 931
(b)
Area of the 2 squares
= 2 x 50 x 50
= 5000 m
2 Area of the top and bottom bases
= 2 x 137 x 50
= 13700 m
2 Area of 1 L-shaped side
= 137 x 1 + (50 - 1) x 4
= 137 + 196
= 333 m
2Area of 2 L-shaped sides
= 2 x 333
= 666 m
2 Total surface area
= 13700 + 5000 + 666
= 19366 m
2 Answer(s): (a) 931; (b) 19366 m
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