SOLUTION: 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 =

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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 =       Log On


   

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.
Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fsqrt%28W%29
Therefore, with V = 30, L = 20, H = 4, and W = 9, then V+=+kLH%2Fsqrt%28W%29 becomes: 30+=+k%2820%29%284%29%2Fsqrt%289%29

30+=+80k%2F3

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

k+=+90%2F80, or k+=+9%2F8

Now, with k+=+9%2F8, and with W = 16, L = 44, and H = 8, then V (volume) = %289%2F8%29%2844%29%288%29%2Fsqrt%2816%29 ------ 396%2F4, or highlight_green%2899m%5E3%29

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