The figure shows a metallic cuboid that measures 137 m by 23 m by 23 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
= 23 ÷ 7
= 3 r 2
Maximum number of 7 m cubes
= 19 x 3 x 3
= 171
(b)
Area of the 2 squares
= 2 x 23 x 23
= 1058 m
2 Area of the top and bottom bases
= 2 x 137 x 23
= 6302 m
2 Area of 1 L-shaped side
= 137 x 2 + (23 - 2) x 4
= 274 + 84
= 358 m
2Area of 2 L-shaped sides
= 2 x 358
= 716 m
2 Total surface area
= 6302 + 1058 + 716
= 8076 m
2 Answer(s): (a) 171; (b) 8076 m
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