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Question

There are 2 cubes A and B each of volume X cm3. Cube B is cut into smaller cubes each of volume Y cm3. 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


A

S1 is true but S2 is false

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B

S1 is false but S2 is true

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C

S1 and S2 are true

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D

S1 and S2 are false

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Solution

The correct option is A

S1 is true but S2 is false


Volume is the space occupied by a body. So cutting an object does not change its volume. Therefore cube A and cube B after cutting will have the same volume.

The surface area of a body depends on the area of surfaces. Since cutting a body creates new surfaces, the surface area of the newly formed cubes would be greater than that of cube A.

Let us try to understand this by converting variables to numbers.

Assume X=64 cm3 and Y=1 cm3.

Number of cubes
=641=64

Volume of cube A
=64 cm3

Volume of cube B after cutting
=64×1=64 cm3

Hence the volume is same.

Length of side of cube A
=364=4 cm

Surface area of cube A
=6×42=96 cm2

Length of cube B after cutting =1 cm

Surface area of 1 cube
=6×12=6 cm2

Surface area of 64 such cubes
=64×6=384 cm2

Hence surface areas are not same.

S1 is true and S2 is false


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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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