The figure shows a metallic cuboid that measures 126 cm by 14 cm by 14 cm.
- Find the maximum number of 5-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
= 126 ÷ 5
= 25 r 1
Breath = Height
Number of cubes along the breadth or height
= 14 ÷ 5
= 2 r 4
Maximum number of 5 cm cubes
= 25 x 2 x 2
= 100
(b)
Area of the 2 squares
= 2 x 14 x 14
= 392 cm
2 Area of the top and bottom bases
= 2 x 126 x 14
= 3528 cm
2 Area of 1 L-shaped side
= 126 x 4 + (14 - 4) x 1
= 504 + 10
= 514 cm
2Area of 2 L-shaped sides
= 2 x 514
= 1028 cm
2 Total surface area
= 3528 + 392 + 1028
= 4948 cm
2 Answer(s): (a) 100; (b) 4948 cm
2