The figure shows a rubber cuboid that measures 117 cm by 37 cm by 37 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
= 117 ÷ 4
= 29 r 1
Breath = Height
Number of cubes along the breadth or height
= 37 ÷ 4
= 9 r 1
Maximum number of 4 cm cubes
= 29 x 9 x 9
= 2349
(b)
Area of the 2 squares
= 2 x 37 x 37
= 2738 cm
2 Area of the top and bottom bases
= 2 x 117 x 37
= 8658 cm
2 Area of 1 L-shaped side
= 117 x 1 + (37 - 1) x 1
= 117 + 36
= 153 cm
2Area of 2 L-shaped sides
= 2 x 153
= 306 cm
2 Total surface area
= 8658 + 2738 + 306
= 11702 cm
2 Answer(s): (a) 2349; (b) 11702 cm
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