The figure shows a rubber cuboid that measures 111 m by 24 m by 24 m.
- Find the maximum number of 9-m cubes that can be cut from the rubber cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 111 ÷ 9
= 12 r 3
Breath = Height
Number of cubes along the breadth or height
= 24 ÷ 9
= 2 r 6
Maximum number of 9 m cubes
= 12 x 2 x 2
= 48
(b)
Area of the 2 squares
= 2 x 24 x 24
= 1152 m
2 Area of the top and bottom bases
= 2 x 111 x 24
= 5328 m
2 Area of 1 L-shaped side
= 111 x 6 + (24 - 6) x 3
= 666 + 54
= 720 m
2Area of 2 L-shaped sides
= 2 x 720
= 1440 m
2 Total surface area
= 5328 + 1152 + 1440
= 7920 m
2 Answer(s): (a) 48; (b) 7920 m
2