Question

ampe
If the area of the circle is increased by 21%, then what
is the percentage increased in the circumference of
the circle?​

Answer 1

Answer:

Please see the attachment

Answer 2

Given:

Area of the circle is increased by 21%

To Find:

The percentage increased in the circumference

Solution

Find the new radius:

$\text{Area of the circle =} \pi r^2$

The area is increased by 21%

Let the new radius with the increased area be x

$\pi x^2 = 1.21(\pi r^2)$

$x^2 = 1.21 r^2$

$x = 1.1r$

Find the new circumference:

$\text{Circumference} = 2\pi r$

The new radius is 1.1r:

$\text{New Circumference} = 2\pi (1.1r)$

$\text{New Circumference} = 2.2\pi r$

Find the percentage increased:

$\text{Percentage Increased} = \dfrac{2.2\pi r - 2\pi r }{2 \pi r} \times 100$

$\text{Percentage Increased} = \dfrac{0.2\pi r }{2 \pi r} \times 100$

$\text{Percentage Increased} = \dfrac{0.2 }{2} \times 100$

$\text{Percentage Increased} = 10 \%$

$\boxed {\boxed {\text{Answer: There is a 10\% increased in the circumference }}}$