The figure shows a metallic cuboid that measures 122 cm by 41 cm by 41 cm.
- Find the maximum number of 3-cm cubes that can be cut from the metallic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 122 ÷ 3
= 40 r 2
Breath = Height
Number of cubes along the breadth or height
= 41 ÷ 3
= 13 r 2
Maximum number of 3 cm cubes
= 40 x 13 x 13
= 6760
(b)
Area of the 2 squares
= 2 x 41 x 41
= 3362 cm
2 Area of the top and bottom bases
= 2 x 122 x 41
= 10004 cm
2 Area of 1 L-shaped side
= 122 x 2 + (41 - 2) x 2
= 244 + 78
= 322 cm
2Area of 2 L-shaped sides
= 2 x 322
= 644 cm
2 Total surface area
= 10004 + 3362 + 644
= 14010 cm
2 Answer(s): (a) 6760; (b) 14010 cm
2