Question

There is a cube of each side 3 cm, which is painted in Red. Now each edge is divided into 3 parts so that the resultant cubes have each edge of 1 cm. Now we have to paint all the new cube sides which are not painted (i.e. the newly cut sides), in blue. How much new area needs to be painted?

Answer 1

Given :- There is a cube of each side 3 cm, which is painted in Red. Now each edge is divided into 3 parts so that the resultant cubes have each edge of 1 cm. Now we have to paint all the new cube sides which are not painted (i.e. the newly cut sides), in blue. How much new area needs to be painted ?

Solution :-

when a cube of 3 cm , is cut into edge of 1 cm.

→ Total number of smaller cubes so formed are = (3)³ /(1)³ = 27 / 1 = 27 cubes.

Now, in these 27 cubes , we have given that, painted in red , So,

• Total number of smaller cubes whose 3 sides painted in red are = 8
• Total number of smaller cubes whose 2 sides painted in red are = 4 + 3 + 3 + 2 = 12
• Total number of smaller cubes whose 1 sides painted in red are = 6 (Middle one.)
• Total number of smaller cubes whose no side painted in red is = 1 .

Now, we know that, a cube have total 6 sides.

So,

• Total number of smaller cubes whose 3 sides pained , now we have to paint rest 3 sides , which covers area of paint = 8 cubes * 3 sides each * ( 1 cm² as area of each) = 8 * 3 * 1 = 24 cm².
• Similarly, area to be pained cubes of 2 sides painted in red = 4 * 12 * 1 = 48 cm².
• area to be painted in blue of cubes whose 1 side is red = 6 * 5 * 1 = 30 cm².
• area to be pained of 1 cube in blue all 6 sides = 6 * 1 = 6 cm².

Therefore,

• Total area painted in blue is = 24 + 48 + 30 + 6 = 108 cm².

Hence, new area needs to be painted in blue is 108 cm².

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