The radii of two circles are 19 cm and 9 cm respectively. The radius o...
28 because
Let the radius of required circle =r cm
Radius of 1st circle r1=9 cm
Radius of 2nd circle r2=19 cm
As per the question
Circumference of the required circle = Sum of circumference of two circles
Circumference of small circle =2πr1
=2π×9
=18π
Circumference of small circle =2πr2
=2π×19
=38π
Now,
Circumference of the required circle = Sum of circumference of two circles
2πr=18π+38π
2πr=58π
r=2π56π
r=28 cm
Hence, radius of new circle is 28 cm.
The radii of two circles are 19 cm and 9 cm respectively. The radius o...
Given:
Radii of two circles = 19 cm and 9 cm
Let the radius of the third circle be 'r'
To find: Radius of the circle which has its circumference equal to the sum of the circumferences of the two circles.
Solution:
1. Circumference of a circle = 2πr
2. Circumference of first circle = 2π(19) = 38π
3. Circumference of second circle = 2π(9) = 18π
4. Sum of circumferences of two circles = 38π + 18π = 56π
5. To find the radius of the third circle, we need to equate its circumference with the sum of the circumferences of the other two circles.
6. So, 2πr = 56π
7. Solving for 'r', we get r = 28 cm.
Therefore, the radius of the circle which has its circumference equal to the sum of the circumferences of the two circles is 28 cm (Option A).