The figure shows a metallic cuboid that measures 106 cm by 26 cm by 26 cm.
- Find the maximum number of 3-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
= 106 ÷ 3
= 35 r 1
Breath = Height
Number of cubes along the breadth or height
= 26 ÷ 3
= 8 r 2
Maximum number of 3 cm cubes
= 35 x 8 x 8
= 2240
(b)
Area of the 2 squares
= 2 x 26 x 26
= 1352 cm
2 Area of the top and bottom bases
= 2 x 106 x 26
= 5512 cm
2 Area of 1 L-shaped side
= 106 x 2 + (26 - 2) x 1
= 212 + 24
= 236 cm
2Area of 2 L-shaped sides
= 2 x 236
= 472 cm
2 Total surface area
= 5512 + 1352 + 472
= 7336 cm
2 Answer(s): (a) 2240; (b) 7336 cm
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