The figure shows a wooden cuboid that measures 133 cm by 23 cm by 23 cm.
- Find the maximum number of 3-cm cubes that can be cut from the wooden cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 133 ÷ 3
= 44 r 1
Breath = Height
Number of cubes along the breadth or height
= 23 ÷ 3
= 7 r 2
Maximum number of 3 cm cubes
= 44 x 7 x 7
= 2156
(b)
Area of the 2 squares
= 2 x 23 x 23
= 1058 cm
2 Area of the top and bottom bases
= 2 x 133 x 23
= 6118 cm
2 Area of 1 L-shaped side
= 133 x 2 + (23 - 2) x 1
= 266 + 21
= 287 cm
2Area of 2 L-shaped sides
= 2 x 287
= 574 cm
2 Total surface area
= 6118 + 1058 + 574
= 7750 cm
2 Answer(s): (a) 2156; (b) 7750 cm
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