The figure shows a metallic cuboid that measures 137 cm by 38 cm by 38 cm.
- Find the maximum number of 7-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
= 137 ÷ 7
= 19 r 4
Breath = Height
Number of cubes along the breadth or height
= 38 ÷ 7
= 5 r 3
Maximum number of 7 cm cubes
= 19 x 5 x 5
= 475
(b)
Area of the 2 squares
= 2 x 38 x 38
= 2888 cm
2 Area of the top and bottom bases
= 2 x 137 x 38
= 10412 cm
2 Area of 1 L-shaped side
= 137 x 3 + (38 - 3) x 4
= 411 + 140
= 551 cm
2Area of 2 L-shaped sides
= 2 x 551
= 1102 cm
2 Total surface area
= 10412 + 2888 + 1102
= 14402 cm
2 Answer(s): (a) 475; (b) 14402 cm
2 
