Question

If each edge of a cube is halved,it's surface area will ​

Answer 1

Answer:

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Step-by-step explanation:

total surface area of a cuboid, with  l, b  and  h  as the length, breadth and height respectively is  2(lb+bh+lh).  

In case of a cube,  l=b=h=s  and hence, the surface area is  6s2.  

Case 1: The length of only one edge of the cube is halved.

The cube now becomes a cuboid with the lengths of edges  s,s  and  s2.  

⇒  Its surface area would be  2(s2+s22+s22)=4s2. Case 2: The lengths of two edges of the cube are halved.

⇒  The new surface area would be two-third the old surface area.

Case 2: The lengths of two edges of the cube are halved

The cube now becomes a cuboid with the lengths of edges  s,s2  and  s2.  

⇒  Its surface area would be  2(s22+s22+s24)=5s22.  

⇒  The new surface area would be five-twelfth the old surface area.

Case 3: The lengths of all the edges of the cube are halved.

The cube now becomes a cube with the lengths of all edges  s2.  

⇒  Its surface area would be  6(s2)2=3s22.  

⇒  The new surface area would be one-fourth the old surface area.