The figure shows a plastic cuboid that measures 102 cm by 14 cm by 14 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
= 102 ÷ 8
= 12 r 6
Breath = Height
Number of cubes along the breadth or height
= 14 ÷ 8
= 1 r 6
Maximum number of 8 cm cubes
= 12 x 1 x 1
= 12
(b)
Area of the 2 squares
= 2 x 14 x 14
= 392 cm
2 Area of the top and bottom bases
= 2 x 102 x 14
= 2856 cm
2 Area of 1 L-shaped side
= 102 x 6 + (14 - 6) x 6
= 612 + 48
= 660 cm
2Area of 2 L-shaped sides
= 2 x 660
= 1320 cm
2 Total surface area
= 2856 + 392 + 1320
= 4568 cm
2 Answer(s): (a) 12; (b) 4568 cm
2