[poll id=”140″]
ANSWER: C. 21%
The circumference of a circle can be expressed with the following formula: C=2π*r
Notice how this means the radius is proportional to the circumference. This means that a percentage increase in the circumference will have the same percentage increase in the radius. Thus, if the circumference increases by 10%, so does the radius. Insert a random value for the radius. For this example, 10 will be used. If we were to increase the circumference by 10%, the radius (10) must also be increased by 10%. 10% of 10 is 1, thus an additional 10% of 10 will be 11.
The area of a circle can be expressed with the following formula: A=π(r^2). If we insert our original radius value of 10, our area will be: π(10^2)= 100π
The area of our modified and expanded circle will be: π(11^2)= 121π
To find the percentage increase: [(121π-100π)/(100π)] x 100 = 21%