a cube of side 2 cm is cut to form small cubes of side 1 cm. the volume of each of the smaller cubes will be

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Dear student,
$s i d e o f s m a l l c u b e = 1 c m = a s i d e o f b i g c u b e = 2 c m = a_{1} v o l u m e o f s m a l l c u b e = a^{3} = 1 c m^{3} v o l u m e o f b i g c u b e = {a_{1}}^{3} = 8 c m^{3} t o t a l s m a l l c u b e s = \frac{v o l u m e o f b i g c u b e}{v o l u m e o f s m a l l c u b e} = 8 c u b e s$

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Question 8
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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a cube of side 2 cm is cut to form small cubes of side 1 cm. the volume of each of the smaller cubes will be

Dear student, side of small cube =1cm=aside of big cube =2cm=a1volume of small cube =a3=1cm3volume of big cube =a13=8cm3total small cubes =volume of big cubevolume of small cube =8 cubes Regards