SOLUTION: The volume of a car, V, is directly proportional to the square of its length, l. Calculate the percentage increase in V when l is doubled.

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Question 550154: The volume of a car, V, is directly proportional to the square of its length, l. Calculate the percentage increase in V when l is doubled.
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
direct proportion's formula is y=kx. In this case y=V and x=length squared
V=k%2Al%5E2
Let's say the length was 10 and k was 1
V=1%2A%28l0%29%5E2
v=1%2A100
vs
v=1%2A%2820%29%5E2
v=1*400
400 is a 300% increase using the formula new minus old over old or (400-100)/100=3=300%
Now let's do the general case. Percent increase is new minus old over old
V=k%2Al%5E2
vs
V=k%2A%282l%29%5E2
V=k%2A4%28l%5E2%29
new minus old over old:
%28k%2A4%28l%5E2%29-k%2A%28l%5E2%29%29%2F%28k%2A%28l%5E2%29%29
k%2A3%28l%5E2%29%2F%28k%2A%28l%5E2%29%29
The k and l^2 cancel out and we are left with 3 which is equal to 300%