The figure shows a plastic cuboid that measures 112 cm by 50 cm by 50 cm.
- Find the maximum number of 6-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
= 112 ÷ 6
= 18 r 4
Breath = Height
Number of cubes along the breadth or height
= 50 ÷ 6
= 8 r 2
Maximum number of 6 cm cubes
= 18 x 8 x 8
= 1152
(b)
Area of the 2 squares
= 2 x 50 x 50
= 5000 cm
2 Area of the top and bottom bases
= 2 x 112 x 50
= 11200 cm
2 Area of 1 L-shaped side
= 112 x 2 + (50 - 2) x 4
= 224 + 192
= 416 cm
2Area of 2 L-shaped sides
= 2 x 416
= 832 cm
2 Total surface area
= 11200 + 5000 + 832
= 17032 cm
2 Answer(s): (a) 1152; (b) 17032 cm
2