The diameter of a circle is increased so that the circumference increases by 70%. By what percent does the area increase?
+1262 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 \(34.6020761...\)
+23252 Formula for the area of a circle: Area = pi·diameter2/4
Old circumference = d ---> old area = pi·d2/4
New circumference = 1.7d ---> new area = pi·(1.7·d)2/4 = 2.89·pi·d2/4
To find the percentage increase, we first need to find the amount of increase:
amount of increase = new area - old area
= 2.89·pi·d2/4 - pi·d2/4
= 1.89·pi·d2/4
Now, we need to divide the amount of increase by the old area:
percentage increase = ( 1.89·pi·d2/4 ) / ( pi·d2/4 )
= 1.89
As a percentage: 189% increase
