The figure shows a metallic cuboid that measures 121 cm by 34 cm by 34 cm.
- Find the maximum number of 7-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
= 121 ÷ 7
= 17 r 2
Breath = Height
Number of cubes along the breadth or height
= 34 ÷ 7
= 4 r 6
Maximum number of 7 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 121 x 34
= 8228 cm
2 Area of 1 L-shaped side
= 121 x 6 + (34 - 6) x 2
= 726 + 56
= 782 cm
2Area of 2 L-shaped sides
= 2 x 782
= 1564 cm
2 Total surface area
= 8228 + 2312 + 1564
= 12104 cm
2 Answer(s): (a) 272; (b) 12104 cm
2