The figure shows a wooden cuboid that measures 100 cm by 36 cm by 36 cm.
- Find the maximum number of 8-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
= 100 ÷ 8
= 12 r 4
Breath = Height
Number of cubes along the breadth or height
= 36 ÷ 8
= 4 r 4
Maximum number of 8 cm cubes
= 12 x 4 x 4
= 192
(b)
Area of the 2 squares
= 2 x 36 x 36
= 2592 cm
2 Area of the top and bottom bases
= 2 x 100 x 36
= 7200 cm
2 Area of 1 L-shaped side
= 100 x 4 + (36 - 4) x 4
= 400 + 128
= 528 cm
2Area of 2 L-shaped sides
= 2 x 528
= 1056 cm
2 Total surface area
= 7200 + 2592 + 1056
= 10848 cm
2 Answer(s): (a) 192; (b) 10848 cm
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