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When 0.5 cm was planed off each of the six faces of a wooden cube, its volume decreased by 169cm^3. Find its new volume.

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When 0.5 cm was planed off each of the six faces of a wooden cube, its volume decreased by 169cm^3. Find its new volume.

Sep 26, 2014

#1
+101424
+11

Let's call the original volume Vo ......... and let's call the new volume Vn

And Vo  = s = Vn + 169    where s is the original side length

Note that, if .5 cm is shaved off each face, then each side is now just (s-1)cm long......so we have...

Vn = (s - 1)3 =  s3 - 3s2 + 3s - 1       and substituting Vn + 169 for s3   we have

Vn = [ Vn + 169] - 3s2 + 3s - 1      and subtracting Vn  from both sides and rearranging, we have

3s2 - 3s - 168  = 0     divide both sides by 3

s2 - s - 56 = 0   factor this

(s - 8)(s +7) = 0   so, s = 8   or  s = -7     (reject the negative answer)

So, s = 8  and that's the original side length

So the new side length = (s - 1) = (8 - 1 )  = 7 .....  and the new volume is 73 = 343cm3

Note that the original volume = 83 = 512cm3

And 512cm3 - 343cm3 = 169cm3   .....and that's the difference between the old volume and the new volume !!!

Sep 26, 2014

#1
+101424
+11

Let's call the original volume Vo ......... and let's call the new volume Vn

And Vo  = s = Vn + 169    where s is the original side length

Note that, if .5 cm is shaved off each face, then each side is now just (s-1)cm long......so we have...

Vn = (s - 1)3 =  s3 - 3s2 + 3s - 1       and substituting Vn + 169 for s3   we have

Vn = [ Vn + 169] - 3s2 + 3s - 1      and subtracting Vn  from both sides and rearranging, we have

3s2 - 3s - 168  = 0     divide both sides by 3

s2 - s - 56 = 0   factor this

(s - 8)(s +7) = 0   so, s = 8   or  s = -7     (reject the negative answer)

So, s = 8  and that's the original side length

So the new side length = (s - 1) = (8 - 1 )  = 7 .....  and the new volume is 73 = 343cm3

Note that the original volume = 83 = 512cm3

And 512cm3 - 343cm3 = 169cm3   .....and that's the difference between the old volume and the new volume !!!

CPhill Sep 26, 2014