The figure shows a rubber cuboid that measures 116 cm by 43 cm by 43 cm.
- Find the maximum number of 3-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
= 116 ÷ 3
= 38 r 2
Breath = Height
Number of cubes along the breadth or height
= 43 ÷ 3
= 14 r 1
Maximum number of 3 cm cubes
= 38 x 14 x 14
= 7448
(b)
Area of the 2 squares
= 2 x 43 x 43
= 3698 cm
2 Area of the top and bottom bases
= 2 x 116 x 43
= 9976 cm
2 Area of 1 L-shaped side
= 116 x 1 + (43 - 1) x 2
= 116 + 84
= 200 cm
2Area of 2 L-shaped sides
= 2 x 200
= 400 cm
2 Total surface area
= 9976 + 3698 + 400
= 14074 cm
2 Answer(s): (a) 7448; (b) 14074 cm
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