The figure shows a rubber cuboid that measures 122 m by 21 m by 21 m.
- Find the maximum number of 6-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
= 122 ÷ 6
= 20 r 2
Breath = Height
Number of cubes along the breadth or height
= 21 ÷ 6
= 3 r 3
Maximum number of 6 m cubes
= 20 x 3 x 3
= 180
(b)
Area of the 2 squares
= 2 x 21 x 21
= 882 m
2 Area of the top and bottom bases
= 2 x 122 x 21
= 5124 m
2 Area of 1 L-shaped side
= 122 x 3 + (21 - 3) x 2
= 366 + 36
= 402 m
2Area of 2 L-shaped sides
= 2 x 402
= 804 m
2 Total surface area
= 5124 + 882 + 804
= 6810 m
2 Answer(s): (a) 180; (b) 6810 m
2