The figure shows a plastic cuboid that measures 124 cm by 30 cm by 30 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
= 124 ÷ 9
= 13 r 7
Breath = Height
Number of cubes along the breadth or height
= 30 ÷ 9
= 3 r 3
Maximum number of 9 cm cubes
= 13 x 3 x 3
= 117
(b)
Area of the 2 squares
= 2 x 30 x 30
= 1800 cm
2 Area of the top and bottom bases
= 2 x 124 x 30
= 7440 cm
2 Area of 1 L-shaped side
= 124 x 3 + (30 - 3) x 7
= 372 + 189
= 561 cm
2Area of 2 L-shaped sides
= 2 x 561
= 1122 cm
2 Total surface area
= 7440 + 1800 + 1122
= 10362 cm
2 Answer(s): (a) 117; (b) 10362 cm
2