The figure shows a metallic cuboid that measures 111 cm by 37 cm by 37 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
= 111 ÷ 8
= 13 r 7
Breath = Height
Number of cubes along the breadth or height
= 37 ÷ 8
= 4 r 5
Maximum number of 8 cm cubes
= 13 x 4 x 4
= 208
(b)
Area of the 2 squares
= 2 x 37 x 37
= 2738 cm
2 Area of the top and bottom bases
= 2 x 111 x 37
= 8214 cm
2 Area of 1 L-shaped side
= 111 x 5 + (37 - 5) x 7
= 555 + 224
= 779 cm
2Area of 2 L-shaped sides
= 2 x 779
= 1558 cm
2 Total surface area
= 8214 + 2738 + 1558
= 12510 cm
2 Answer(s): (a) 208; (b) 12510 cm
2