The figure shows a rubber cuboid that measures 148 cm by 21 cm by 21 cm.
- Find the maximum number of 8-cm cubes that can be cut from the rubber cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 148 ÷ 8
= 18 r 4
Breath = Height
Number of cubes along the breadth or height
= 21 ÷ 8
= 2 r 5
Maximum number of 8 cm cubes
= 18 x 2 x 2
= 72
(b)
Area of the 2 squares
= 2 x 21 x 21
= 882 cm
2 Area of the top and bottom bases
= 2 x 148 x 21
= 6216 cm
2 Area of 1 L-shaped side
= 148 x 5 + (21 - 5) x 4
= 740 + 64
= 804 cm
2Area of 2 L-shaped sides
= 2 x 804
= 1608 cm
2 Total surface area
= 6216 + 882 + 1608
= 8706 cm
2 Answer(s): (a) 72; (b) 8706 cm
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