The figure shows a metallic cuboid that measures 130 cm by 21 cm by 21 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
= 130 ÷ 9
= 14 r 4
Breath = Height
Number of cubes along the breadth or height
= 21 ÷ 9
= 2 r 3
Maximum number of 9 cm cubes
= 14 x 2 x 2
= 56
(b)
Area of the 2 squares
= 2 x 21 x 21
= 882 cm
2 Area of the top and bottom bases
= 2 x 130 x 21
= 5460 cm
2 Area of 1 L-shaped side
= 130 x 3 + (21 - 3) x 4
= 390 + 72
= 462 cm
2Area of 2 L-shaped sides
= 2 x 462
= 924 cm
2 Total surface area
= 5460 + 882 + 924
= 7266 cm
2 Answer(s): (a) 56; (b) 7266 cm
2