The figure shows a rubber cuboid that measures 103 m by 18 m by 18 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
= 103 ÷ 8
= 12 r 7
Breath = Height
Number of cubes along the breadth or height
= 18 ÷ 8
= 2 r 2
Maximum number of 8 m cubes
= 12 x 2 x 2
= 48
(b)
Area of the 2 squares
= 2 x 18 x 18
= 648 m
2 Area of the top and bottom bases
= 2 x 103 x 18
= 3708 m
2 Area of 1 L-shaped side
= 103 x 2 + (18 - 2) x 7
= 206 + 112
= 318 m
2Area of 2 L-shaped sides
= 2 x 318
= 636 m
2 Total surface area
= 3708 + 648 + 636
= 4992 m
2 Answer(s): (a) 48; (b) 4992 m
2