Question

what happen to the volume of a cube when it's edges is (a) tripled (b) one third

Answer 1

let the edge of the original cube be x

in the given condition,new edge will be 3x

(a)if tripled,
volume of original cube =x×x×x
$= {x}^{3}$
volume of new cube =3x×3x×3x
=(3x)^3
$= 27x {}^{3}$
now the number of times volume increases ,
$= \frac{27x { }^{3} }{ {x}^{3} }$

=volume will increase 27 times.

(b)one third
let original edge=x
new edge
$new \: edge \: = x \ \frac{1}{3}$
$volume \: = {x}^{3}$
$new \: volume \: = \frac{x}{3} \times \frac{x}{3{} } \times \frac{x}{3}$
$= \frac{ {x}^{3} }{27}$
therefore,
number of times
x^3÷x^3/27
=1/27
the volume will be 1/27 th of the the original volume which is x^3

Answer 2

Answer:

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