The figure shows a wooden cuboid that measures 112 m by 17 m by 17 m.
- Find the maximum number of 9-m 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
= 112 ÷ 9
= 12 r 4
Breath = Height
Number of cubes along the breadth or height
= 17 ÷ 9
= 1 r 8
Maximum number of 9 m cubes
= 12 x 1 x 1
= 12
(b)
Area of the 2 squares
= 2 x 17 x 17
= 578 m
2 Area of the top and bottom bases
= 2 x 112 x 17
= 3808 m
2 Area of 1 L-shaped side
= 112 x 8 + (17 - 8) x 4
= 896 + 36
= 932 m
2Area of 2 L-shaped sides
= 2 x 932
= 1864 m
2 Total surface area
= 3808 + 578 + 1864
= 6250 m
2 Answer(s): (a) 12; (b) 6250 m
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