Math, asked by msd56, 6 months ago

If each side of a cube is increased by 25% whay will be the ratio of the the volume of the new cube to that of the original one?​

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Answered by Selvarasen
0

Answer:

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Answered by Anonymous
3

\bf{\underline{Question}}

If each side of a cube is increased by 25%. What will be the ratio of the volume of the new cube to that of the original one.

\bf{\underline{Assumption}}

Let the side of the original cube be x

\bf{\underline{Solution}}

Side of original cube = x

\sf{Volume\:of\:original\:cube\:(V_1)= (x)^3 = x^3\:cubic\:units}

Now,

Each Side of the cube is increased by 25%

Therefore,

Side of new cube:-

= \sf{x+25\%\:of\:x}

= \sf{x+ x \times \dfrac{25}{100}}

= \sf{x+x\times\dfrac{1}{4}}

= \sf{x+\dfrac{x}{4}}

= \sf{\dfrac{4x+x}{4}}

= \sf{\dfrac{5x}{4}}

\sf{\therefore} The side of new cube is \sf{\dfrac{5x}{4}}

Hence,

\sf{Volume\:of\:new\:cube\:(V_2) = \bigg(\dfrac{5x}{4}\bigg)^3 }

= \sf{Volume\:of\:new\:cube\:(V_2) = \dfrac{125x^3}{64}\:cubic\:units}

Now,

Ratio of volume of new cube to that of original cube:-

= \sf{V_1:V_2}

= \sf{\dfrac{125x^3}{64}:x^3}

= \sf{\dfrac{125x^3}{\dfrac{64}{x^3}}}

= \sf{\dfrac{125x^3}{64}\times\dfrac{1}{x^3}}

= \sf{\dfrac{125}{64}}

= \sf{125:64}

\sf{\therefore} The ratio of volume of new cube to that of original cube is 125:64

\bf{\underline{Extra\:Information}}

  • \sf{Volume\:of\:Cube = (side)^3\:cubic\:units}

  • \sf{TSA\:of\:cube=6a^2\:\:sq.units}

  • \sf{LSA\:of\:cube=4a^2\:\:sq.units}

\bf{\underline{Note}}

  • TSA stands for Total Surface Area
  • LSA stands for Lateral Surface Area
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