The figure shows a metallic cuboid that measures 131 cm by 41 cm by 41 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
= 131 ÷ 9
= 14 r 5
Breath = Height
Number of cubes along the breadth or height
= 41 ÷ 9
= 4 r 5
Maximum number of 9 cm cubes
= 14 x 4 x 4
= 224
(b)
Area of the 2 squares
= 2 x 41 x 41
= 3362 cm
2 Area of the top and bottom bases
= 2 x 131 x 41
= 10742 cm
2 Area of 1 L-shaped side
= 131 x 5 + (41 - 5) x 5
= 655 + 180
= 835 cm
2Area of 2 L-shaped sides
= 2 x 835
= 1670 cm
2 Total surface area
= 10742 + 3362 + 1670
= 15774 cm
2 Answer(s): (a) 224; (b) 15774 cm
2