if the radius of a circle increases by 6%. what is the percentage increasein its area and circumference?

Answer 1

Area = pi (radius)^2
if radius increase by 6%
Area1 = pi (1.06radius)^2
Area1 = 1.1236pi(radius)^2
So Area incerase by 12.36%

Circumference = 2pi(radius)
if radius increase by 6%
Circumference1 = 2pi(1.06radius)
Circumference1 = 1.06(2pi)(radius)
So Cicumference increase by 6%

Answer 2

It would also be 6%

Answer 3

The circumference increase is also 6% but area is 6% squared, that is about 12,36 % more ( 6% = 1,06 ; 1,06 x 1,06 = 1.1236 = 12.36%)

Answer 4

so - we make two problems

radius of 100 and 106

circumference is pi (diameter)
Area is pi (radius ) (radius)

take the resulting figures of the 100 and divide by the 106

to find your respective increases for both area and circumference

Answer 5

Area of original circle = πr² where r is radius
6% = 6/100 = 0 .06
New radius = r + 0.06 r = 1.06 r
New area = π (1.06 r)² = 1.1236 (πr²)
Increase in area = 1.1236(πr²) - πr² = 0.1236πr²
% increase = 12.36%

Circumference = 2πr
New circumference = 2π(1.06r)
Increase = 2πr(1.06 - 1) = 0.06 x (2πr)
% increase = 6%