The figure shows a plastic cuboid that measures 108 cm by 42 cm by 42 cm.
- Find the maximum number of 8-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
= 108 ÷ 8
= 13 r 4
Breath = Height
Number of cubes along the breadth or height
= 42 ÷ 8
= 5 r 2
Maximum number of 8 cm cubes
= 13 x 5 x 5
= 325
(b)
Area of the 2 squares
= 2 x 42 x 42
= 3528 cm
2 Area of the top and bottom bases
= 2 x 108 x 42
= 9072 cm
2 Area of 1 L-shaped side
= 108 x 2 + (42 - 2) x 4
= 216 + 160
= 376 cm
2Area of 2 L-shaped sides
= 2 x 376
= 752 cm
2 Total surface area
= 9072 + 3528 + 752
= 13352 cm
2 Answer(s): (a) 325; (b) 13352 cm
2