The figure shows a plastic cuboid that measures 107 cm by 11 cm by 11 cm.
- Find the maximum number of 6-cm cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 107 ÷ 6
= 17 r 5
Breath = Height
Number of cubes along the breadth or height
= 11 ÷ 6
= 1 r 5
Maximum number of 6 cm cubes
= 17 x 1 x 1
= 17
(b)
Area of the 2 squares
= 2 x 11 x 11
= 242 cm
2 Area of the top and bottom bases
= 2 x 107 x 11
= 2354 cm
2 Area of 1 L-shaped side
= 107 x 5 + (11 - 5) x 5
= 535 + 30
= 565 cm
2Area of 2 L-shaped sides
= 2 x 565
= 1130 cm
2 Total surface area
= 2354 + 242 + 1130
= 3726 cm
2 Answer(s): (a) 17; (b) 3726 cm
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