The figure shows a plastic cuboid that measures 136 cm by 22 cm by 22 cm.
- Find the maximum number of 3-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
= 136 ÷ 3
= 45 r 1
Breath = Height
Number of cubes along the breadth or height
= 22 ÷ 3
= 7 r 1
Maximum number of 3 cm cubes
= 45 x 7 x 7
= 2205
(b)
Area of the 2 squares
= 2 x 22 x 22
= 968 cm
2 Area of the top and bottom bases
= 2 x 136 x 22
= 5984 cm
2 Area of 1 L-shaped side
= 136 x 1 + (22 - 1) x 1
= 136 + 21
= 157 cm
2Area of 2 L-shaped sides
= 2 x 157
= 314 cm
2 Total surface area
= 5984 + 968 + 314
= 7266 cm
2 Answer(s): (a) 2205; (b) 7266 cm
2