The figure shows a plastic cuboid that measures 102 cm by 49 cm by 49 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
= 102 ÷ 4
= 25 r 2
Breath = Height
Number of cubes along the breadth or height
= 49 ÷ 4
= 12 r 1
Maximum number of 4 cm cubes
= 25 x 12 x 12
= 3600
(b)
Area of the 2 squares
= 2 x 49 x 49
= 4802 cm
2 Area of the top and bottom bases
= 2 x 102 x 49
= 9996 cm
2 Area of 1 L-shaped side
= 102 x 1 + (49 - 1) x 2
= 102 + 96
= 198 cm
2Area of 2 L-shaped sides
= 2 x 198
= 396 cm
2 Total surface area
= 9996 + 4802 + 396
= 15194 cm
2 Answer(s): (a) 3600; (b) 15194 cm
2