The radii of two circles are 19 cm and 9 cm respectively. Find the radius and area of the circles which has it circumference equal to the sum of the circumferences of the two circles.
Answers
Answer:
The Radius of the circle is 28 cm & Area of a circle is 2464 cm² .
Step-by-step explanation:
SOLUTION :
Let the radius of the two circles be r1 & r2.
Given :
Radius of first circle ,r1 = 19 cm
Radius of first circle ,r2 = 9 cm
Circumference of first circle , C1 = 2πr1
C1 = 2π × 19
C1 = 38 π cm …………(1)
Circumference of second circle , C2 = 2πr2
C2 = 2π × 9
C2 = 18 π cm …………(2)
Circumference of circle, C = 2πr
Circumference of circle = Sum of the Circumferences of the two circles (Given)
C = C1 + C2
2πr = 38π + 18π
[From eq 1 & 2]
2πr = π(38 + 18)
2r = 56
r = 56/2 = 28
r = 28 cm
Radius of the circle,r = 28 cm
Area of a circle, A = πr²
A = 22/7 × 28 × 28
A = 22 × 28 × 4 = 88 × 28 = 2464 cm²
Area of a circle = 2464 cm² .
Hence, the Radius of the circle is 28 cm & Area of a circle is 2464 cm² .
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Answer:
radius (R1) = 28cm
Area = 2464cm²
Explanation:
Let R ,r are radii of two circles.
R = 19cm , r = 9cm
Let the radius of the new circle be R1.
According to the problem given,
Circumference of the new circle = 2πR + 2πr
=> 2πR1 = 2π(R+r)
=> R1 = R+r
=> R1 = 19cm + 9cm
=> R1 = 28 cm
Now ,
Area of the new circle = π(R1)²
= (22/7 ) × (28)²
= 22 × 28 × 4
= 2464 cm²
Therefore,
Required radius (R1) = 28cm
Area = 2464cm²
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