Total surface area of a cube is $54 {c m}^{2}$ . Then its side is _____ $c m$ .

6

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Solution

The correct option is D $3$
Let the side of the cube be $a c m$
Surface area of a cube is given by $6 a^{2}$
So according to question $6 a^{2} = 54$
so $a^{2} = 9$ and $a = 3 c m$

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A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

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Solution:

Side(a) of the cube = 12 cm

Volume of the cube =(a)3=(12 cm)3=1728 cm3

Let the side of the smaller cube be a1.

Volume of 1 smaller cube =(17288)cm3=216 cm3(a1)3=216 cm3⇒a1=6 cm

Therefore, the side of the smaller cubes will be 6 cm.

Ratio between surface areas of cubes =Surface area of bigger cubeSurface area of Smaller cube=6×1226×62=(12)2(6)2=41

Therefore, the ratio between the surface areas of these cubes is 4:1.

my doubt is how this a1 got 6cm

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Total surface area of a cube is 54 cm2. Then its side is _____ cm.

The correct option is D 3Let the side of the cube be a cmSurface area of a cube is given by 6a2So according to question 6a2=54so a2=9 and a=3 cm

Total surface area of a cube is $54 {c m}^{2}$ . Then its side is _____ $c m$ .

The correct option is D $3$
Let the side of the cube be $a c m$
Surface area of a cube is given by $6 a^{2}$
So according to question $6 a^{2} = 54$
so $a^{2} = 9$ and $a = 3 c m$