Question

when each edge of a cube is decreased by 1 cm, its volume is decreased by 91 cm^3 .Find the length of the a side of the original cube. HELP ME PLZ PEOPLE!!!!!!!!!!!!!!!!!!

Answer 1

Answer:

6cm

Step-by-step explanation:

Let length of side of original cube be x

Original volume = $x^{3}$

new volume = $(x-1)^{3}$

$(x-1)^{3}$ = $x^{3}$ - 91

$x^{3}$ - 1 - 3x(x-1) = $x^{3}$- 91

-1 - 3$x^{2}$ + $3x$ = -91

$3x^{2} - 3x - 90 = 0$

$3x^{2} - 18x + 15x - 90$

$3x(x-6) + 15(x-6) = 0$

$(3x+15)(x-6)=0$

$3x+15=0$   or   $x-6=0$

but since x cant be negative, we neglect the first one.

thus x = 6

so side of original cube is 6cm

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