The figure shows a rubber cuboid that measures 113 cm by 11 cm by 11 cm.
- Find the maximum number of 5-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 ÷ 5
= 22 r 3
Breath = Height
Number of cubes along the breadth or height
= 11 ÷ 5
= 2 r 1
Maximum number of 5 cm cubes
= 22 x 2 x 2
= 88
(b)
Area of the 2 squares
= 2 x 11 x 11
= 242 cm
2 Area of the top and bottom bases
= 2 x 113 x 11
= 2486 cm
2 Area of 1 L-shaped side
= 113 x 1 + (11 - 1) x 3
= 113 + 30
= 143 cm
2Area of 2 L-shaped sides
= 2 x 143
= 286 cm
2 Total surface area
= 2486 + 242 + 286
= 3014 cm
2 Answer(s): (a) 88; (b) 3014 cm
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