The figure shows a wooden cuboid that measures 103 cm by 47 cm by 47 cm.
- Find the maximum number of 5-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
= 103 ÷ 5
= 20 r 3
Breath = Height
Number of cubes along the breadth or height
= 47 ÷ 5
= 9 r 2
Maximum number of 5 cm cubes
= 20 x 9 x 9
= 1620
(b)
Area of the 2 squares
= 2 x 47 x 47
= 4418 cm
2 Area of the top and bottom bases
= 2 x 103 x 47
= 9682 cm
2 Area of 1 L-shaped side
= 103 x 2 + (47 - 2) x 3
= 206 + 135
= 341 cm
2Area of 2 L-shaped sides
= 2 x 341
= 682 cm
2 Total surface area
= 9682 + 4418 + 682
= 14782 cm
2 Answer(s): (a) 1620; (b) 14782 cm
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