If each edge of a cube is doubled find-(i) how many times will its surface area increase? (ii) how many times will its volume increase?
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Hi ,
Let the edge of a cube = a units
i )surface area ( A ) =6a sq units ---( 1 )
ii ) volume ( V ) = a³ cubic units--( 2 )
If edge of a cube is doubled,
iii) New cube surface area = 6 × 2a
= 2 × 6a
= 2 × A [ from ( 1 ) ]
= 2 times of the first cube
iv ) volume of a new cube = ( 2a )³
= 8a³
= 8 × V [ from ( 2 ) ]
= 8 times of the first cube
I hope this helps you.
: )
Let the edge of a cube = a units
i )surface area ( A ) =6a sq units ---( 1 )
ii ) volume ( V ) = a³ cubic units--( 2 )
If edge of a cube is doubled,
iii) New cube surface area = 6 × 2a
= 2 × 6a
= 2 × A [ from ( 1 ) ]
= 2 times of the first cube
iv ) volume of a new cube = ( 2a )³
= 8a³
= 8 × V [ from ( 2 ) ]
= 8 times of the first cube
I hope this helps you.
: )
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