The figure shows a metallic cuboid that measures 107 cm by 33 cm by 33 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
= 107 ÷ 8
= 13 r 3
Breath = Height
Number of cubes along the breadth or height
= 33 ÷ 8
= 4 r 1
Maximum number of 8 cm cubes
= 13 x 4 x 4
= 208
(b)
Area of the 2 squares
= 2 x 33 x 33
= 2178 cm
2 Area of the top and bottom bases
= 2 x 107 x 33
= 7062 cm
2 Area of 1 L-shaped side
= 107 x 1 + (33 - 1) x 3
= 107 + 96
= 203 cm
2Area of 2 L-shaped sides
= 2 x 203
= 406 cm
2 Total surface area
= 7062 + 2178 + 406
= 9646 cm
2 Answer(s): (a) 208; (b) 9646 cm
2