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Question

A cube with edges of length b is divided into 8 equal smaller cubes. Calculate the difference between the combined surface area of the 8 smaller cubes and the surface area of the original cube.

A
32b2
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B
34b2
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C
92b2
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D
6b2
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E
12b2
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Solution

The correct option is C 6b2
Surface area of original cube is 6b2
Volume of cube is b3
Volume of smaller cube is b38, which implies side length of smaller cube is b2
Surface area of 8 smaller cubes combined is 8×6×b22=12b2
Difference is 12b26b2=6b2

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Q. Question:

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.

Mathematics Surface Areas and Volumes Volume of Solids
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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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