The figure shows a rubber cuboid that measures 110 m by 42 m by 42 m.
- Find the maximum number of 8-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
= 110 ÷ 8
= 13 r 6
Breath = Height
Number of cubes along the breadth or height
= 42 ÷ 8
= 5 r 2
Maximum number of 8 m cubes
= 13 x 5 x 5
= 325
(b)
Area of the 2 squares
= 2 x 42 x 42
= 3528 m
2 Area of the top and bottom bases
= 2 x 110 x 42
= 9240 m
2 Area of 1 L-shaped side
= 110 x 2 + (42 - 2) x 6
= 220 + 240
= 460 m
2Area of 2 L-shaped sides
= 2 x 460
= 920 m
2 Total surface area
= 9240 + 3528 + 920
= 13688 m
2 Answer(s): (a) 325; (b) 13688 m
2