Question

if the length of side cube is dobuled
then the ratio of volume of new cube
​

Answer 1

A n s w e r

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G i v e n

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• Length of side of cube is doubled

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F i n d

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• Ratio of volume of new cube

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S o l u t i o n

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We know that ,

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$\underline{\bold{\texttt{Volume of cube :}}}$

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➠ a³ ⚊⚊⚊⚊ ⓵

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Where ,

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• a = Side of cube

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$\underline{\bold{\texttt{Original volume :}}}$

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Let the original length of side be "z"

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• a = z

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⟮ Putting the above values ⓵ ⟯

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➜ a³

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➜ z³ ⚊⚊⚊⚊ ⓶

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• Hence the original volume of cube is z³ cu. unit

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$\underline{\bold{\texttt{New volume :}}}$

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Length of side cube is doubled

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• a = 2z

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⟮ Putting the above values in ⓵ ⟯

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➜ a³

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➜ (2z)³

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➜ 8z³ ⚊⚊⚊⚊ ⓷

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• Hence the new volume of cube is 8z³ cu. unit

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$\underline{\bold{\texttt{Ratio of volume }}}$

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➜ $\sf \dfrac { 8z ^3 } { z ^3 }$

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➨ $\sf \dfrac { 8 } { 1 }$

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∴ The ratio of the new volume to the original volume is 8:1

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