The figure shows a plastic cuboid that measures 131 cm by 26 cm by 26 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
= 131 ÷ 4
= 32 r 3
Breath = Height
Number of cubes along the breadth or height
= 26 ÷ 4
= 6 r 2
Maximum number of 4 cm cubes
= 32 x 6 x 6
= 1152
(b)
Area of the 2 squares
= 2 x 26 x 26
= 1352 cm
2 Area of the top and bottom bases
= 2 x 131 x 26
= 6812 cm
2 Area of 1 L-shaped side
= 131 x 2 + (26 - 2) x 3
= 262 + 72
= 334 cm
2Area of 2 L-shaped sides
= 2 x 334
= 668 cm
2 Total surface area
= 6812 + 1352 + 668
= 8832 cm
2 Answer(s): (a) 1152; (b) 8832 cm
2