The figure shows a metallic cuboid that measures 122 cm by 46 cm by 46 cm.
- Find the maximum number of 3-cm cubes that can be cut from the metallic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 122 ÷ 3
= 40 r 2
Breath = Height
Number of cubes along the breadth or height
= 46 ÷ 3
= 15 r 1
Maximum number of 3 cm cubes
= 40 x 15 x 15
= 9000
(b)
Area of the 2 squares
= 2 x 46 x 46
= 4232 cm
2 Area of the top and bottom bases
= 2 x 122 x 46
= 11224 cm
2 Area of 1 L-shaped side
= 122 x 1 + (46 - 1) x 2
= 122 + 90
= 212 cm
2Area of 2 L-shaped sides
= 2 x 212
= 424 cm
2 Total surface area
= 11224 + 4232 + 424
= 15880 cm
2 Answer(s): (a) 9000; (b) 15880 cm
2