The figure shows a wooden cuboid that measures 109 cm by 19 cm by 19 cm.
- Find the maximum number of 6-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
= 109 ÷ 6
= 18 r 1
Breath = Height
Number of cubes along the breadth or height
= 19 ÷ 6
= 3 r 1
Maximum number of 6 cm cubes
= 18 x 3 x 3
= 162
(b)
Area of the 2 squares
= 2 x 19 x 19
= 722 cm
2 Area of the top and bottom bases
= 2 x 109 x 19
= 4142 cm
2 Area of 1 L-shaped side
= 109 x 1 + (19 - 1) x 1
= 109 + 18
= 127 cm
2Area of 2 L-shaped sides
= 2 x 127
= 254 cm
2 Total surface area
= 4142 + 722 + 254
= 5118 cm
2 Answer(s): (a) 162; (b) 5118 cm
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