The figure shows a plastic cuboid that measures 130 cm by 16 cm by 16 cm.
- Find the maximum number of 6-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
= 130 ÷ 6
= 21 r 4
Breath = Height
Number of cubes along the breadth or height
= 16 ÷ 6
= 2 r 4
Maximum number of 6 cm cubes
= 21 x 2 x 2
= 84
(b)
Area of the 2 squares
= 2 x 16 x 16
= 512 cm
2 Area of the top and bottom bases
= 2 x 130 x 16
= 4160 cm
2 Area of 1 L-shaped side
= 130 x 4 + (16 - 4) x 4
= 520 + 48
= 568 cm
2Area of 2 L-shaped sides
= 2 x 568
= 1136 cm
2 Total surface area
= 4160 + 512 + 1136
= 5808 cm
2 Answer(s): (a) 84; (b) 5808 cm
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