The figure shows a rubber cuboid that measures 110 cm by 47 cm by 47 cm.
- Find the maximum number of 4-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
= 110 ÷ 4
= 27 r 2
Breath = Height
Number of cubes along the breadth or height
= 47 ÷ 4
= 11 r 3
Maximum number of 4 cm cubes
= 27 x 11 x 11
= 3267
(b)
Area of the 2 squares
= 2 x 47 x 47
= 4418 cm
2 Area of the top and bottom bases
= 2 x 110 x 47
= 10340 cm
2 Area of 1 L-shaped side
= 110 x 3 + (47 - 3) x 2
= 330 + 88
= 418 cm
2Area of 2 L-shaped sides
= 2 x 418
= 836 cm
2 Total surface area
= 10340 + 4418 + 836
= 15594 cm
2 Answer(s): (a) 3267; (b) 15594 cm
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