The figure shows a plastic cuboid that measures 140 cm by 49 cm by 49 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
= 140 ÷ 8
= 17 r 4
Breath = Height
Number of cubes along the breadth or height
= 49 ÷ 8
= 6 r 1
Maximum number of 8 cm cubes
= 17 x 6 x 6
= 612
(b)
Area of the 2 squares
= 2 x 49 x 49
= 4802 cm
2 Area of the top and bottom bases
= 2 x 140 x 49
= 13720 cm
2 Area of 1 L-shaped side
= 140 x 1 + (49 - 1) x 4
= 140 + 192
= 332 cm
2Area of 2 L-shaped sides
= 2 x 332
= 664 cm
2 Total surface area
= 13720 + 4802 + 664
= 19186 cm
2 Answer(s): (a) 612; (b) 19186 cm
2