The figure shows a plastic cuboid that measures 146 cm by 14 cm by 14 cm.
- Find the maximum number of 4-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
= 146 ÷ 4
= 36 r 2
Breath = Height
Number of cubes along the breadth or height
= 14 ÷ 4
= 3 r 2
Maximum number of 4 cm cubes
= 36 x 3 x 3
= 324
(b)
Area of the 2 squares
= 2 x 14 x 14
= 392 cm
2 Area of the top and bottom bases
= 2 x 146 x 14
= 4088 cm
2 Area of 1 L-shaped side
= 146 x 2 + (14 - 2) x 2
= 292 + 24
= 316 cm
2Area of 2 L-shaped sides
= 2 x 316
= 632 cm
2 Total surface area
= 4088 + 392 + 632
= 5112 cm
2 Answer(s): (a) 324; (b) 5112 cm
2