The figure shows a rubber cuboid that measures 113 cm by 31 cm by 31 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
= 113 ÷ 3
= 37 r 2
Breath = Height
Number of cubes along the breadth or height
= 31 ÷ 3
= 10 r 1
Maximum number of 3 cm cubes
= 37 x 10 x 10
= 3700
(b)
Area of the 2 squares
= 2 x 31 x 31
= 1922 cm
2 Area of the top and bottom bases
= 2 x 113 x 31
= 7006 cm
2 Area of 1 L-shaped side
= 113 x 1 + (31 - 1) x 2
= 113 + 60
= 173 cm
2Area of 2 L-shaped sides
= 2 x 173
= 346 cm
2 Total surface area
= 7006 + 1922 + 346
= 9274 cm
2 Answer(s): (a) 3700; (b) 9274 cm
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