The figure shows a plastic cuboid that measures 144 cm by 38 cm by 38 cm.
- Find the maximum number of 5-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
= 144 ÷ 5
= 28 r 4
Breath = Height
Number of cubes along the breadth or height
= 38 ÷ 5
= 7 r 3
Maximum number of 5 cm cubes
= 28 x 7 x 7
= 1372
(b)
Area of the 2 squares
= 2 x 38 x 38
= 2888 cm
2 Area of the top and bottom bases
= 2 x 144 x 38
= 10944 cm
2 Area of 1 L-shaped side
= 144 x 3 + (38 - 3) x 4
= 432 + 140
= 572 cm
2Area of 2 L-shaped sides
= 2 x 572
= 1144 cm
2 Total surface area
= 10944 + 2888 + 1144
= 14976 cm
2 Answer(s): (a) 1372; (b) 14976 cm
2