The figure shows a rubber cuboid that measures 134 m by 31 m by 31 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
= 134 ÷ 6
= 22 r 2
Breath = Height
Number of cubes along the breadth or height
= 31 ÷ 6
= 5 r 1
Maximum number of 6 m cubes
= 22 x 5 x 5
= 550
(b)
Area of the 2 squares
= 2 x 31 x 31
= 1922 m
2 Area of the top and bottom bases
= 2 x 134 x 31
= 8308 m
2 Area of 1 L-shaped side
= 134 x 1 + (31 - 1) x 2
= 134 + 60
= 194 m
2Area of 2 L-shaped sides
= 2 x 194
= 388 m
2 Total surface area
= 8308 + 1922 + 388
= 10618 m
2 Answer(s): (a) 550; (b) 10618 m
2