The figure shows a wooden cuboid that measures 146 m by 11 m by 11 m.
- Find the maximum number of 4-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
= 146 ÷ 4
= 36 r 2
Breath = Height
Number of cubes along the breadth or height
= 11 ÷ 4
= 2 r 3
Maximum number of 4 m cubes
= 36 x 2 x 2
= 144
(b)
Area of the 2 squares
= 2 x 11 x 11
= 242 m
2 Area of the top and bottom bases
= 2 x 146 x 11
= 3212 m
2 Area of 1 L-shaped side
= 146 x 3 + (11 - 3) x 2
= 438 + 16
= 454 m
2Area of 2 L-shaped sides
= 2 x 454
= 908 m
2 Total surface area
= 3212 + 242 + 908
= 4362 m
2 Answer(s): (a) 144; (b) 4362 m
2