The figure shows a metallic cuboid that measures 133 cm by 31 cm by 31 cm.
- Find the maximum number of 9-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
= 133 ÷ 9
= 14 r 7
Breath = Height
Number of cubes along the breadth or height
= 31 ÷ 9
= 3 r 4
Maximum number of 9 cm cubes
= 14 x 3 x 3
= 126
(b)
Area of the 2 squares
= 2 x 31 x 31
= 1922 cm
2 Area of the top and bottom bases
= 2 x 133 x 31
= 8246 cm
2 Area of 1 L-shaped side
= 133 x 4 + (31 - 4) x 7
= 532 + 189
= 721 cm
2Area of 2 L-shaped sides
= 2 x 721
= 1442 cm
2 Total surface area
= 8246 + 1922 + 1442
= 11610 cm
2 Answer(s): (a) 126; (b) 11610 cm
2