Asked by Joel
The diameter of a circle is increased by enough to increase the circumference by 20%. By what % is the area of the circle increased ? ( Hint: Try a number like t=5.)
Answers
Answered by
Reiny
original radius ---- r
original circumference ---- 2πr
new circumference = 1.2(2πr) = 2.4πr or 2π(1.2r)
new radius = 1.2r
old area = πr^2
new area = π(1.2r^2 = 1.44πr^2
change in area = .44πr^2
percentage change = .44πr^2/πr^2 = .44 or 44%
The above shows the increase to be 44% for all values,
taking r = 5 would show it to be 44% for that value, it does not prove it to be true for all values
original circumference ---- 2πr
new circumference = 1.2(2πr) = 2.4πr or 2π(1.2r)
new radius = 1.2r
old area = πr^2
new area = π(1.2r^2 = 1.44πr^2
change in area = .44πr^2
percentage change = .44πr^2/πr^2 = .44 or 44%
The above shows the increase to be 44% for all values,
taking r = 5 would show it to be 44% for that value, it does not prove it to be true for all values
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