The figure shows a wooden cuboid that measures 101 cm by 21 cm by 21 cm.
- Find the maximum number of 4-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
= 101 ÷ 4
= 25 r 1
Breath = Height
Number of cubes along the breadth or height
= 21 ÷ 4
= 5 r 1
Maximum number of 4 cm cubes
= 25 x 5 x 5
= 625
(b)
Area of the 2 squares
= 2 x 21 x 21
= 882 cm
2 Area of the top and bottom bases
= 2 x 101 x 21
= 4242 cm
2 Area of 1 L-shaped side
= 101 x 1 + (21 - 1) x 1
= 101 + 20
= 121 cm
2Area of 2 L-shaped sides
= 2 x 121
= 242 cm
2 Total surface area
= 4242 + 882 + 242
= 5366 cm
2 Answer(s): (a) 625; (b) 5366 cm
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