The figure shows a wooden cuboid that measures 125 m by 23 m by 23 m.
- Find the maximum number of 8-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
= 125 ÷ 8
= 15 r 5
Breath = Height
Number of cubes along the breadth or height
= 23 ÷ 8
= 2 r 7
Maximum number of 8 m cubes
= 15 x 2 x 2
= 60
(b)
Area of the 2 squares
= 2 x 23 x 23
= 1058 m
2 Area of the top and bottom bases
= 2 x 125 x 23
= 5750 m
2 Area of 1 L-shaped side
= 125 x 7 + (23 - 7) x 5
= 875 + 80
= 955 m
2Area of 2 L-shaped sides
= 2 x 955
= 1910 m
2 Total surface area
= 5750 + 1058 + 1910
= 8718 m
2 Answer(s): (a) 60; (b) 8718 m
2