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If a cube with length, height and width equal to $10\; cm$, is reduced to a smaller cube of height, length and width of $9\; cm$ then reduction in volume is :

  1. $172\;cm^3$
  2. $729 \;cm^3$
  3. $271\;cm^3$
  4. None of the options
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A cube is a rectangular solid whose length, width and height are equal.

Volume of cube $ V = a^{3},$ where $a = $ side length of cube

Now, $V_{1} = 10^{3}\:\text{cm}^{3} = 1000\:\text{cm}^{3},$ and $V_{2} = 9^{3}\:\text{cm}^{3} = 729\:\text{cm}^{3}$

Reduction in volume $ = V_{1} – V_{2} = 1000 – 729 = 271\:\text{cm}^{3}.$

So, the correct answer is $(C).$

Ref: https://brilliant.org/wiki/volume-problem-solving-easy/

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initial side = 10

volume = a*a*a= 10*10*10 = 1000

nw side = 9

new volume = 9*9*9=729

change in volume = ( initial- final)

1000-729=271

hence  c is correct
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