The figure shows a metallic cuboid that measures 131 cm by 50 cm by 50 cm.
- Find the maximum number of 7-cm 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
= 131 ÷ 7
= 18 r 5
Breath = Height
Number of cubes along the breadth or height
= 50 ÷ 7
= 7 r 1
Maximum number of 7 cm cubes
= 18 x 7 x 7
= 882
(b)
Area of the 2 squares
= 2 x 50 x 50
= 5000 cm
2 Area of the top and bottom bases
= 2 x 131 x 50
= 13100 cm
2 Area of 1 L-shaped side
= 131 x 1 + (50 - 1) x 5
= 131 + 245
= 376 cm
2Area of 2 L-shaped sides
= 2 x 376
= 752 cm
2 Total surface area
= 13100 + 5000 + 752
= 18852 cm
2 Answer(s): (a) 882; (b) 18852 cm
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