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 =
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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) (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:
Therefore, with V = 30, L = 20, H = 4, and W = 9, then becomes:
80k = 90 ------ Cross-multiplying
, or
Now, with , and with W = 16, L = 44, and H = 8, then V (volume) = ------ , or
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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