The figure shows a plastic cuboid that measures 138 cm by 35 cm by 35 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
= 138 ÷ 8
= 17 r 2
Breath = Height
Number of cubes along the breadth or height
= 35 ÷ 8
= 4 r 3
Maximum number of 8 cm cubes
= 17 x 4 x 4
= 272
(b)
Area of the 2 squares
= 2 x 35 x 35
= 2450 cm
2 Area of the top and bottom bases
= 2 x 138 x 35
= 9660 cm
2 Area of 1 L-shaped side
= 138 x 3 + (35 - 3) x 2
= 414 + 64
= 478 cm
2Area of 2 L-shaped sides
= 2 x 478
= 956 cm
2 Total surface area
= 9660 + 2450 + 956
= 13066 cm
2 Answer(s): (a) 272; (b) 13066 cm
2