The figure shows a plastic cuboid that measures 104 cm by 39 cm by 39 cm.
- Find the maximum number of 6-cm cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 104 ÷ 6
= 17 r 2
Breath = Height
Number of cubes along the breadth or height
= 39 ÷ 6
= 6 r 3
Maximum number of 6 cm cubes
= 17 x 6 x 6
= 612
(b)
Area of the 2 squares
= 2 x 39 x 39
= 3042 cm
2 Area of the top and bottom bases
= 2 x 104 x 39
= 8112 cm
2 Area of 1 L-shaped side
= 104 x 3 + (39 - 3) x 2
= 312 + 72
= 384 cm
2Area of 2 L-shaped sides
= 2 x 384
= 768 cm
2 Total surface area
= 8112 + 3042 + 768
= 11922 cm
2 Answer(s): (a) 612; (b) 11922 cm
2