The figure shows a rubber cuboid that measures 140 cm by 50 cm by 50 cm.
- Find the maximum number of 3-cm 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
= 140 ÷ 3
= 46 r 2
Breath = Height
Number of cubes along the breadth or height
= 50 ÷ 3
= 16 r 2
Maximum number of 3 cm cubes
= 46 x 16 x 16
= 11776
(b)
Area of the 2 squares
= 2 x 50 x 50
= 5000 cm
2 Area of the top and bottom bases
= 2 x 140 x 50
= 14000 cm
2 Area of 1 L-shaped side
= 140 x 2 + (50 - 2) x 2
= 280 + 96
= 376 cm
2Area of 2 L-shaped sides
= 2 x 376
= 752 cm
2 Total surface area
= 14000 + 5000 + 752
= 19752 cm
2 Answer(s): (a) 11776; (b) 19752 cm
2