The figure shows a metallic cuboid that measures 134 cm by 46 cm by 46 cm.
- Find the maximum number of 8-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
= 134 ÷ 8
= 16 r 6
Breath = Height
Number of cubes along the breadth or height
= 46 ÷ 8
= 5 r 6
Maximum number of 8 cm cubes
= 16 x 5 x 5
= 400
(b)
Area of the 2 squares
= 2 x 46 x 46
= 4232 cm
2 Area of the top and bottom bases
= 2 x 134 x 46
= 12328 cm
2 Area of 1 L-shaped side
= 134 x 6 + (46 - 6) x 6
= 804 + 240
= 1044 cm
2Area of 2 L-shaped sides
= 2 x 1044
= 2088 cm
2 Total surface area
= 12328 + 4232 + 2088
= 18648 cm
2 Answer(s): (a) 400; (b) 18648 cm
2