The figure shows a metallic cuboid that measures 109 cm by 41 cm by 41 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
= 109 ÷ 8
= 13 r 5
Breath = Height
Number of cubes along the breadth or height
= 41 ÷ 8
= 5 r 1
Maximum number of 8 cm cubes
= 13 x 5 x 5
= 325
(b)
Area of the 2 squares
= 2 x 41 x 41
= 3362 cm
2 Area of the top and bottom bases
= 2 x 109 x 41
= 8938 cm
2 Area of 1 L-shaped side
= 109 x 1 + (41 - 1) x 5
= 109 + 200
= 309 cm
2Area of 2 L-shaped sides
= 2 x 309
= 618 cm
2 Total surface area
= 8938 + 3362 + 618
= 12918 cm
2 Answer(s): (a) 325; (b) 12918 cm
2