The figure shows a rubber cuboid that measures 138 cm by 48 cm by 48 cm.
- Find the maximum number of 5-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
= 138 ÷ 5
= 27 r 3
Breath = Height
Number of cubes along the breadth or height
= 48 ÷ 5
= 9 r 3
Maximum number of 5 cm cubes
= 27 x 9 x 9
= 2187
(b)
Area of the 2 squares
= 2 x 48 x 48
= 4608 cm
2 Area of the top and bottom bases
= 2 x 138 x 48
= 13248 cm
2 Area of 1 L-shaped side
= 138 x 3 + (48 - 3) x 3
= 414 + 135
= 549 cm
2Area of 2 L-shaped sides
= 2 x 549
= 1098 cm
2 Total surface area
= 13248 + 4608 + 1098
= 18954 cm
2 Answer(s): (a) 2187; (b) 18954 cm
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