Question

find the diameter of circle whose area is equal to the sum of the area of two circle of diameter 20cm and 48cm​

Answer 1

Answer:

Area of circle = area of circle with radius 10cm + area of circle with radius 24

πr^2= π10^2+ π*24^2

πr^2= π(100+576)

r^2=676

r=√676=26

diameter =2r=2*26= 52cm

Answer 2

let the diameter be d

let us consider the circles as:-

O, A, B

it is given that

ar (O)=ar (A) + ar (B)

diameter of circle A d_A=20cm

area (circle )=

$\pi {( \frac{d}{2})  }^{2}$

Therefore area(A)=100$\pi$

and area(B)=576$\pi$

sum of both the areas is equal to the area of circle O

Therefore, we can write-

$\pi  {( \frac{d}{2} )}^{2}  = 100\pi + 576\pi </p><p>(\frac{d}{2})^{2}  = (676) </p><p>[tex]\frac{d}{2}=26\\d=52 cm$