The figure shows a plastic cuboid that measures 117 cm by 12 cm by 12 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
= 117 ÷ 8
= 14 r 5
Breath = Height
Number of cubes along the breadth or height
= 12 ÷ 8
= 1 r 4
Maximum number of 8 cm cubes
= 14 x 1 x 1
= 14
(b)
Area of the 2 squares
= 2 x 12 x 12
= 288 cm
2 Area of the top and bottom bases
= 2 x 117 x 12
= 2808 cm
2 Area of 1 L-shaped side
= 117 x 4 + (12 - 4) x 5
= 468 + 40
= 508 cm
2Area of 2 L-shaped sides
= 2 x 508
= 1016 cm
2 Total surface area
= 2808 + 288 + 1016
= 4112 cm
2 Answer(s): (a) 14; (b) 4112 cm
2