Suppose each face of a 3cm X 5cm X 4cm block of wood is shaven down by x cm. If the shaved block has half the original volume, find the value of x to the nearest hundredth.

Question

paxpolaris · Answer

what's the original volume?

anonymous · Answer

well (3)(4)(5)=60 therefore 60

paxpolaris · Answer

well then if you subtract x from each side you get: 
3-x, 4-x, 5-x

anonymous · Answer

would i multiply them together and set it up to 30?

paxpolaris · Answer

yes

anonymous · Answer

Thank you!

anonymous · Answer

@PaxPolaris  can I do something like: 
the shaved one has volume 30
so, the taken out part has volume is 30 also, so that x*x*x =30 and get x by that way?

anonymous · Answer

That's what I was thinking but I wasn't sure

anonymous · Answer

Also once I set the equation up, would I distribute and solve or is there a more efficient way?

paxpolaris · Answer

@OOOPS no x^3 =30 won't work

anonymous · Answer

can i graph this equation on my calculator and find the maximum of the x value @PaxPolaris

anonymous · Answer

oh yea, I see my mistake. I am sorry. You are right. @PaxPolaris

paxpolaris · Answer

yes, i think you have to graph to get the answer

 find the point of intersection of $ y= (3-x)(4-x)(5-x)$ and $y=30$
 or see where $y= (3-x)(4-x)(5-x)-30$ meets the x-axis

anonymous · Answer

I got x=0.78

paxpolaris · Answer

yep . :)

anonymous · Answer

Thank you so much!