The figure shows a metallic cuboid that measures 102 cm by 27 cm by 27 cm.
- Find the maximum number of 8-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
= 102 ÷ 8
= 12 r 6
Breath = Height
Number of cubes along the breadth or height
= 27 ÷ 8
= 3 r 3
Maximum number of 8 cm cubes
= 12 x 3 x 3
= 108
(b)
Area of the 2 squares
= 2 x 27 x 27
= 1458 cm
2 Area of the top and bottom bases
= 2 x 102 x 27
= 5508 cm
2 Area of 1 L-shaped side
= 102 x 3 + (27 - 3) x 6
= 306 + 144
= 450 cm
2Area of 2 L-shaped sides
= 2 x 450
= 900 cm
2 Total surface area
= 5508 + 1458 + 900
= 7866 cm
2 Answer(s): (a) 108; (b) 7866 cm
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