The figure shows a plastic cuboid that measures 142 cm by 34 cm by 34 cm.
- Find the maximum number of 4-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
= 142 ÷ 4
= 35 r 2
Breath = Height
Number of cubes along the breadth or height
= 34 ÷ 4
= 8 r 2
Maximum number of 4 cm cubes
= 35 x 8 x 8
= 2240
(b)
Area of the 2 squares
= 2 x 34 x 34
= 2312 cm
2 Area of the top and bottom bases
= 2 x 142 x 34
= 9656 cm
2 Area of 1 L-shaped side
= 142 x 2 + (34 - 2) x 2
= 284 + 64
= 348 cm
2Area of 2 L-shaped sides
= 2 x 348
= 696 cm
2 Total surface area
= 9656 + 2312 + 696
= 12664 cm
2 Answer(s): (a) 2240; (b) 12664 cm
2