The figure shows a rubber cuboid that measures 143 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
= 143 ÷ 6
= 23 r 5
Breath = Height
Number of cubes along the breadth or height
= 31 ÷ 6
= 5 r 1
Maximum number of 6 m cubes
= 23 x 5 x 5
= 575
(b)
Area of the 2 squares
= 2 x 31 x 31
= 1922 m
2 Area of the top and bottom bases
= 2 x 143 x 31
= 8866 m
2 Area of 1 L-shaped side
= 143 x 1 + (31 - 1) x 5
= 143 + 150
= 293 m
2Area of 2 L-shaped sides
= 2 x 293
= 586 m
2 Total surface area
= 8866 + 1922 + 586
= 11374 m
2 Answer(s): (a) 575; (b) 11374 m
2