Question

Find the area of a circle whose circumference is the sum of the circumferences of two circles with radii 8 and 6 units..

• A.
  $626c{m}^2$
• B.
  $636c{m}^2$
• C.
  $616c{m}^2$
• D.
  $606c{m}^2$

Answer 1

The correct option is C

$616c{m}^2$
Circumference of a circle = $2\pi r$
where $r$ is the radius of the circle.
Given,
Circumference of a 1st circle = $2\pi \times 8=16\pi$ cm
Circumference of a 2nd circle = $2\pi \times 6=12\pi$ cm
$\therefore$ Circumference of the bigger circle = $16\pi +12\pi =28\pi$ cm
So, $2\pi r=28\pi$
$r=14$ cm

Now, area of a circle
= $\pi r^2$
= $\frac{22}{7}\times 14\times 14$
= $616c{m}^2$