The figure shows a metallic cuboid that measures 121 m by 37 m by 37 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
= 121 ÷ 8
= 15 r 1
Breath = Height
Number of cubes along the breadth or height
= 37 ÷ 8
= 4 r 5
Maximum number of 8 m cubes
= 15 x 4 x 4
= 240
(b)
Area of the 2 squares
= 2 x 37 x 37
= 2738 m
2 Area of the top and bottom bases
= 2 x 121 x 37
= 8954 m
2 Area of 1 L-shaped side
= 121 x 5 + (37 - 5) x 1
= 605 + 32
= 637 m
2Area of 2 L-shaped sides
= 2 x 637
= 1274 m
2 Total surface area
= 8954 + 2738 + 1274
= 12966 m
2 Answer(s): (a) 240; (b) 12966 m
2