The figure shows a metallic cuboid that measures 107 cm by 32 cm by 32 cm.
- Find the maximum number of 6-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
= 107 ÷ 6
= 17 r 5
Breath = Height
Number of cubes along the breadth or height
= 32 ÷ 6
= 5 r 2
Maximum number of 6 cm cubes
= 17 x 5 x 5
= 425
(b)
Area of the 2 squares
= 2 x 32 x 32
= 2048 cm
2 Area of the top and bottom bases
= 2 x 107 x 32
= 6848 cm
2 Area of 1 L-shaped side
= 107 x 2 + (32 - 2) x 5
= 214 + 150
= 364 cm
2Area of 2 L-shaped sides
= 2 x 364
= 728 cm
2 Total surface area
= 6848 + 2048 + 728
= 9624 cm
2 Answer(s): (a) 425; (b) 9624 cm
2