Question

The radii of two circles are in the ratio 3 : 8. If the difference between their area is 269$\pi c{m}^2$, Find the area of the smaller circle.

• A. 1386 $c{m}^2$
• B. 1356 $c{m}^2$
• C. 1666 $c{m}^2$
• D. 1686 $c{m}^2$

Answer 1

The correct option is A 1386 $c{m}^2$

Given,ratio of the two circle=$3:8$
Let the radius of the smaller circle be $3x$ and greater circle be $8x$
Now,
$\pi (8x{)}^2-\pi (3x{)}^2=2695\pi$
$=>64x^2-9x^2=2695$
$55x^2=2695$
$=>x^2=49$
$=>x=7$
Therefore,
Area of smaller circle=$\pi (3\times 7{)}^2$
=$\frac{22}{7}\times 21\times 21$
=$1386c{m}^2$