The figure shows a plastic cuboid that measures 122 cm by 43 cm by 43 cm.
- Find the maximum number of 9-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
= 122 ÷ 9
= 13 r 5
Breath = Height
Number of cubes along the breadth or height
= 43 ÷ 9
= 4 r 7
Maximum number of 9 cm cubes
= 13 x 4 x 4
= 208
(b)
Area of the 2 squares
= 2 x 43 x 43
= 3698 cm
2 Area of the top and bottom bases
= 2 x 122 x 43
= 10492 cm
2 Area of 1 L-shaped side
= 122 x 7 + (43 - 7) x 5
= 854 + 180
= 1034 cm
2Area of 2 L-shaped sides
= 2 x 1034
= 2068 cm
2 Total surface area
= 10492 + 3698 + 2068
= 16258 cm
2 Answer(s): (a) 208; (b) 16258 cm
2