The figure shows a wooden cuboid that measures 116 cm by 31 cm by 31 cm.
- Find the maximum number of 9-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
= 116 ÷ 9
= 12 r 8
Breath = Height
Number of cubes along the breadth or height
= 31 ÷ 9
= 3 r 4
Maximum number of 9 cm cubes
= 12 x 3 x 3
= 108
(b)
Area of the 2 squares
= 2 x 31 x 31
= 1922 cm
2 Area of the top and bottom bases
= 2 x 116 x 31
= 7192 cm
2 Area of 1 L-shaped side
= 116 x 4 + (31 - 4) x 8
= 464 + 216
= 680 cm
2Area of 2 L-shaped sides
= 2 x 680
= 1360 cm
2 Total surface area
= 7192 + 1922 + 1360
= 10474 cm
2 Answer(s): (a) 108; (b) 10474 cm
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