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The radii of two circles are 19 cm and 9 cm respectively. Find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.
Given:
The radii of two circles are 19 cm and 9 cm respectively.
To do:
We have to find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.
Solution:
Let the radius of the circle be $r$.
We know that,
Circumference of a circle of radius $r=2 \pi r$
Area of a circle of radius $r=\pi r^2$
Therefore,
The circumference of the circle of radius $19\ cm=2 \pi (19)$
$=38\pi$
The circumference of the circle of radius $9\ cm=2 \pi (9)$
$=18\pi$
According to the question,
$2\pi r=38\pi+18\pi$
$2\pi r=56\pi$
$r=28$
Area of the circle $=\frac{22}{7} \times (28)^2\ cm^2$
$=22\times 112\ cm^2$
$=2464\ cm^2$
The radius and area of the circle are $28\ cm$ and $2464\ cm^2$ respectively.
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