Question 684225
The volume of a solid object varies jointly with the length of the height and inversely with the square root of the width of the object.  If the volume is 30 m^3 when the length = 20 meters, width = 9 meters and the height = 4 meters, find the volume in (m^3) of the solid object when the width is 16 meters and the length is 44 meters and the hight is 8 meters.  

Here is what I understand.  V = K (l)(h)/square root
I plugged in 30m^3 = K (20)(4)/Square root of 9
Then I got 30m^3 = K800 and then I got stuck from there.  I don't know whether to divide 800 on both sides or 30.  I think its 800, so that K = 30^m/800.  After that, the problem seemed like a mess, because the answer is actually 99m^3 and I got 33m^3/20, because I did something totally stupid.  What am I doing wrong?  Thank you in advance for your help.


Since volume varies jointly with the height and length, and inversely with the square root of the width, then: {{{V = kLH/sqrt(W)}}}
Therefore, with V = 30, L = 20, H = 4, and W = 9, then {{{V = kLH/sqrt(W)}}} becomes: {{{30 = k(20)(4)/sqrt(9)}}}


{{{30 = 80k/3}}}


80k = 90 ------ Cross-multiplying


{{{k = 90/80}}}, or {{{k = 9/8}}}


Now, with {{{k = 9/8}}}, and with W = 16, L = 44, and H = 8, then V (volume) = {{{(9/8)(44)(8)/sqrt(16)}}} ------ {{{396/4}}}, or {{{highlight_green(99m^3)}}}


Send comments and “thank-yous” to “D” at MathMadEzy@aol.com