MathematicsThe volume of a cube is 343cm3343cm3. Then, the surface is ____.

The volume of a cube is 343cm3343cm3. Then, the surface is ____.


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    Solution:

    We know that a cuboid is a three dimensional object with six rectangular faces joined by 8 vertices. It has three different types of sides called length, breadth and height denoted  l,b  and  h  . 
    A cube is cuboid with 6 square faces with all sides of equal length. It means  l=b=h=a  volume of a cuboid is l×b×h  . So we calculate the volume of a cube with denoting as  V  .
    V=l×b×h=a×a×a= a 3  
    IMG_256The surface area of the cube is the sum of areas of 6 square faces. The area of 1 square face is a×a= a 2  .
    TSA=6 a 2  
    We are given the question that the volume of a cube is  343c m 2  . Let us denote its volume as  V   and length of the side as  a  . So we have
    V=343c m 3 a 3 =343c m 3  
    a= (343c m 3 ) 1 3 = ( (7cm) 3 ) 1 3 =7cm  
    TSA=6 a 2 TSA=6× (7) 2 TSA=294c m 2  
    Hence, the Surface is 294c m 2  .
     
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