Question

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.
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Answer 1

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 2

According to question

C= C1+ C 2
C=2πr¹+2πr2
C=2*22/7*19 +2*22/7*9
C=22/7(38+18)
C=22/7(56)
C=22*8
C=176 cm


we know that c=2πr

176=2*22/7*r

Required radius=28 cm ,

Area =
πr²=22/7*28*28
=22*4*28
= 2464

Hence area =2464 cm²



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