The figure shows a metallic cuboid that measures 123 cm by 34 cm by 34 cm.
- Find the maximum number of 4-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
= 123 ÷ 4
= 30 r 3
Breath = Height
Number of cubes along the breadth or height
= 34 ÷ 4
= 8 r 2
Maximum number of 4 cm cubes
= 30 x 8 x 8
= 1920
(b)
Area of the 2 squares
= 2 x 34 x 34
= 2312 cm
2 Area of the top and bottom bases
= 2 x 123 x 34
= 8364 cm
2 Area of 1 L-shaped side
= 123 x 2 + (34 - 2) x 3
= 246 + 96
= 342 cm
2Area of 2 L-shaped sides
= 2 x 342
= 684 cm
2 Total surface area
= 8364 + 2312 + 684
= 11360 cm
2 Answer(s): (a) 1920; (b) 11360 cm
2