The figure shows a metallic cuboid that measures 148 cm by 49 cm by 49 cm.
- Find the maximum number of 5-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
= 148 ÷ 5
= 29 r 3
Breath = Height
Number of cubes along the breadth or height
= 49 ÷ 5
= 9 r 4
Maximum number of 5 cm cubes
= 29 x 9 x 9
= 2349
(b)
Area of the 2 squares
= 2 x 49 x 49
= 4802 cm
2 Area of the top and bottom bases
= 2 x 148 x 49
= 14504 cm
2 Area of 1 L-shaped side
= 148 x 4 + (49 - 4) x 3
= 592 + 135
= 727 cm
2Area of 2 L-shaped sides
= 2 x 727
= 1454 cm
2 Total surface area
= 14504 + 4802 + 1454
= 20760 cm
2 Answer(s): (a) 2349; (b) 20760 cm
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