The figure shows a metallic cuboid that measures 141 cm by 34 cm by 34 cm.
- Find the maximum number of 8-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
= 141 ÷ 8
= 17 r 5
Breath = Height
Number of cubes along the breadth or height
= 34 ÷ 8
= 4 r 2
Maximum number of 8 cm cubes
= 17 x 4 x 4
= 272
(b)
Area of the 2 squares
= 2 x 34 x 34
= 2312 cm
2 Area of the top and bottom bases
= 2 x 141 x 34
= 9588 cm
2 Area of 1 L-shaped side
= 141 x 2 + (34 - 2) x 5
= 282 + 160
= 442 cm
2Area of 2 L-shaped sides
= 2 x 442
= 884 cm
2 Total surface area
= 9588 + 2312 + 884
= 12784 cm
2 Answer(s): (a) 272; (b) 12784 cm
2