The figure shows a metallic cuboid that measures 128 cm by 21 cm by 21 cm.
- Find the maximum number of 9-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
= 128 ÷ 9
= 14 r 2
Breath = Height
Number of cubes along the breadth or height
= 21 ÷ 9
= 2 r 3
Maximum number of 9 cm cubes
= 14 x 2 x 2
= 56
(b)
Area of the 2 squares
= 2 x 21 x 21
= 882 cm
2 Area of the top and bottom bases
= 2 x 128 x 21
= 5376 cm
2 Area of 1 L-shaped side
= 128 x 3 + (21 - 3) x 2
= 384 + 36
= 420 cm
2Area of 2 L-shaped sides
= 2 x 420
= 840 cm
2 Total surface area
= 5376 + 882 + 840
= 7098 cm
2 Answer(s): (a) 56; (b) 7098 cm
2