The figure shows a rubber cuboid that measures 149 cm by 46 cm by 46 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
= 149 ÷ 3
= 49 r 2
Breath = Height
Number of cubes along the breadth or height
= 46 ÷ 3
= 15 r 1
Maximum number of 3 cm cubes
= 49 x 15 x 15
= 11025
(b)
Area of the 2 squares
= 2 x 46 x 46
= 4232 cm
2 Area of the top and bottom bases
= 2 x 149 x 46
= 13708 cm
2 Area of 1 L-shaped side
= 149 x 1 + (46 - 1) x 2
= 149 + 90
= 239 cm
2Area of 2 L-shaped sides
= 2 x 239
= 478 cm
2 Total surface area
= 13708 + 4232 + 478
= 18418 cm
2 Answer(s): (a) 11025; (b) 18418 cm
2