The figure shows a plastic cuboid that measures 132 cm by 31 cm by 31 cm.
- Find the maximum number of 5-cm cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 132 ÷ 5
= 26 r 2
Breath = Height
Number of cubes along the breadth or height
= 31 ÷ 5
= 6 r 1
Maximum number of 5 cm cubes
= 26 x 6 x 6
= 936
(b)
Area of the 2 squares
= 2 x 31 x 31
= 1922 cm
2 Area of the top and bottom bases
= 2 x 132 x 31
= 8184 cm
2 Area of 1 L-shaped side
= 132 x 1 + (31 - 1) x 2
= 132 + 60
= 192 cm
2Area of 2 L-shaped sides
= 2 x 192
= 384 cm
2 Total surface area
= 8184 + 1922 + 384
= 10490 cm
2 Answer(s): (a) 936; (b) 10490 cm
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