Question

6. Find the diameter of a circle
whose area is equal to the sum
of areas of two circles with
radii 30 cm and 40 cm
O 300cm
O 200cm
O 150cm
O 100cm​

Answer 1

100cm

A3 = A1+A2

πr3^2= πr1^2 +πr2^2

4

r3^2=r1^2 +r2^2

r3^2= 900+1600

r3= √2500

r3=50cm

diameter =2r

d = 2×50

d=. 100

Answer 2

GIVEN :-

• Radii of two circles ( r ) = 30 cm and 40 cm.

TO FIND :-

• The diameter of a circle whose area is equal to the sum of areas of two circles .

SOLUTION :-

Firstly, Find the area of Circle with radii 30 cm.

⇒ Area of Circle = πr²

⇒ Area of Circle = 22/7 × (30)²

⇒ Area of Circle = 22/7 × 900

⇒ Area of Circle = (22 × 900)/7

⇒ Area of Circle = 19800/7

⇒ Area of Circle = 2828.57 cm²

Similarly, Area of the circle with radii 40 cm.

⇒ Area of Circle = πr²

⇒ Area of Circle = 22/7 × (40)²

⇒ Area of Circle = 22/7 × 1600

⇒ Area of Circle = (22 × 1600)/7

⇒ Area of Circle = 35200/7

⇒ Area of Circle = 5028.57 cm²

Now According to the question , Find the area of Circle whose area is equal to the sum of two Circles,

⇒ Area of Circle = 2828.57 cm² + 5028.57 cm²

⇒ Area of Circle = 7857.14 cm²

Now let's find the diameter of the circle,

⇒ Area of Circle = πr²

⇒ 7857.14 = πr²

⇒ 7857.14 = 3.14 × r²

⇒ r² = 7856.14/3.14

⇒ r² = 2502.27

⇒ r = √2502.27

⇒ r = 50.02 m

⇒ r ≈ 50 m.

Now as we know that the relationship between radius and diameter of the circle,

⇒ d = 2r

⇒ d = 2 × 50

⇒ d = 100 m.

Hence The diameter of a circle whose area is equal to the sum of areas of two circles is 100 m.