The diameter of a circle is increased so that the circumference increases by 70%. By what percent does the area increase?

Guest Jun 4, 2020

#1**+20 **

since the circumfrence increases by 70% the diameter increses by 70% so we get the equation \(\frac{100}{17^2}\) which is \(\frac{100}{289}\)and you multiply it by 100 to get a percent so we get \(\frac{10000}{289}\) and appoxemetly \(34.6020761...\)

jimkey17 Jun 4, 2020

#2**0 **

Formula for the area of a circle: Area = pi·diameter^{2}/4

Old circumference = d ---> old area = pi·d^{2}/4

New circumference = 1.7d ---> new area = pi·(1.7·d)^{2}/4 = 2.89·pi·d^{2}/4

To find the percentage increase, we first need to find the amount of increase:

amount of increase = new area - old area

= 2.89·pi·d^{2}/4 - pi·d^{2}/4

= 1.89·pi·d^{2}/4

Now, we need to divide the amount of increase by the old area:

percentage increase = ( 1.89·pi·d^{2}/4 ) / ( pi·d^{2}/4 )

= 1.89

As a percentage: 189% increase

geno3141 Jun 4, 2020