The figure shows a rubber cuboid that measures 104 m by 39 m by 39 m.
- Find the maximum number of 7-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
= 104 ÷ 7
= 14 r 6
Breath = Height
Number of cubes along the breadth or height
= 39 ÷ 7
= 5 r 4
Maximum number of 7 m cubes
= 14 x 5 x 5
= 350
(b)
Area of the 2 squares
= 2 x 39 x 39
= 3042 m
2 Area of the top and bottom bases
= 2 x 104 x 39
= 8112 m
2 Area of 1 L-shaped side
= 104 x 4 + (39 - 4) x 6
= 416 + 210
= 626 m
2Area of 2 L-shaped sides
= 2 x 626
= 1252 m
2 Total surface area
= 8112 + 3042 + 1252
= 12406 m
2 Answer(s): (a) 350; (b) 12406 m
2