The figure shows a metallic cuboid that measures 111 cm by 23 cm by 23 cm.
- Find the maximum number of 6-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 ÷ 6
= 18 r 3
Breath = Height
Number of cubes along the breadth or height
= 23 ÷ 6
= 3 r 5
Maximum number of 6 cm cubes
= 18 x 3 x 3
= 162
(b)
Area of the 2 squares
= 2 x 23 x 23
= 1058 cm
2 Area of the top and bottom bases
= 2 x 111 x 23
= 5106 cm
2 Area of 1 L-shaped side
= 111 x 5 + (23 - 5) x 3
= 555 + 54
= 609 cm
2Area of 2 L-shaped sides
= 2 x 609
= 1218 cm
2 Total surface area
= 5106 + 1058 + 1218
= 7382 cm
2 Answer(s): (a) 162; (b) 7382 cm
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