The figure shows a metallic cuboid that measures 103 m by 36 m by 36 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
= 103 ÷ 8
= 12 r 7
Breath = Height
Number of cubes along the breadth or height
= 36 ÷ 8
= 4 r 4
Maximum number of 8 m cubes
= 12 x 4 x 4
= 192
(b)
Area of the 2 squares
= 2 x 36 x 36
= 2592 m
2 Area of the top and bottom bases
= 2 x 103 x 36
= 7416 m
2 Area of 1 L-shaped side
= 103 x 4 + (36 - 4) x 7
= 412 + 224
= 636 m
2Area of 2 L-shaped sides
= 2 x 636
= 1272 m
2 Total surface area
= 7416 + 2592 + 1272
= 11280 m
2 Answer(s): (a) 192; (b) 11280 m
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