From a corner of a cube, a smaller cube is cut out. What can you say about the surface area and volume of the remaining portion of the cube?

Volume is constant but surface area changes

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Volume changes but surface area is constant

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Volume and surface area both are constant

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Volume and surface area both change

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Solution

The correct option is B
Volume changes but surface area is constant

Lets name the vertices of the portion cut out.

Faces ABDC, BEHD and ABEF which are part of the bigger cube are removed and due to this, new faces EFGH, AFGC and CGHD are formed. Therefore the surface area remains the same.

But since, a part of the cube is removed, the volume changes.

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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.

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

There are 2 cubes A and B each of volume $X c m^{3}$ . Cube B is cut into smaller cubes each of volume $Y c m^{3}$ . The surface area and volumes of the resulting cubes are compared

S1: The ratio of volumes of A and B = 1:1

S2: The ratio of surface areas of A and B = 1:1

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