Physics Proportion Clarification

[lovesbailey]

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Hi, I was looking through TPR's MCAT Physics & Math review section and came across a Q I don't really understand.

The Q says that the area of a circle of radius r is given be A= πr^2. If r increases by 50%, by what percent will A increase?

The explanation they give is that r increases by r/2, making it 3r/2. Therefore, A increases to (3/2)^2 = 9/4 = 225% times its original value, representing an increase of 225-100=125%.

What I don't understand is why does r go from r to 3r/2. I'm super rusty with math and would really appreciate if someone could clarify this for me. Thanks!

 

[SaintJude]

50% = 0.5 = 1/2
So a 50% increase is an addition of 1/2 of a whole object
So
r =(1)r = (2/2)r
So 50% addition to a whole object can be expressed as : (2/2)r + (1/2)r = 3/2 r

A 100% increase is a doubling of r.

 

[ljc]

To (in my mind) simplify:

"If r increases by 50%"
How do you do this in numerical terms? You multiply "r" by 1.5. What is 3/2? 1.5.


"What I don't understand is why does r go from r to 3r/2"
Think of it as (3/2) * r. Or basically, 1.5*r.

 

[MedPR]

Hi, I was looking through TPR's MCAT Physics & Math review section and came across a Q I don't really understand.

The Q says that the area of a circle of radius r is given be A= πr^2. If r increases by 50%, by what percent will A increase?

The explanation they give is that r increases by r/2, making it 3r/2. Therefore, A increases to (3/2)^2 = 9/4 = 225% times its original value, representing an increase of 225-100=125%.

What I don't understand is why does r go from r to 3r/2. I'm super rusty with math and would really appreciate if someone could clarify this for me. Thanks!

3r/2 is the same thing as 1.5r. Lots of people just prefer to deal with whole numbers and ratios rather than decimals. If you increase 1r by 50%, you've added 1/2 to your original value of 1. So now you have 1.5r.

So, say your radius was 10. Increase it by 50% and now your radius is 15.