the diameter of two circle are 36cm and 20cm respectively find the area of circle which has circumference equal to sum of circumference of two circle. also find the ratio of area of big circle and the sum of area of two circle
Answers
Let the radius of the required circle be 'R'.
Radius of 1st circle = d/2 = 36/2 = 18 cm
Radius of 2nd circle = 20/2 = 10 cm
As given, circumference of biggest circle = circumference of 1st circle + 2nd circle.
=> 2π(18) + 2π(10) = 2πR
=> 2π[18 + 10] = 2πR
=> 18 + 10 = R
=> 28 = R
Area of the biggest circle = πR² = π(28)² Area of the biggest circle = π(784)
= 2464 cm²
Sum of area of 1st + 2nd circle = π(18)² + π(10)² = π(18² + 10²) = π(424)
Required ratio = π(784)/ π(424)
Required ratio = 784/424 = 98/53
Solution!!
The diameter of 2 circles are given as 36 cm ans 20 cm.
We have to find the area of a circle whose circumference is equal to the sum of circumference of the two circles whose diameter is given. So let's find out the circumference of the two circles.
Diameter (d₁) = 36 cm
Radius (r₁) = 36/2 cm = 18 cm
Circumference (c₁) = 2πr
c₁ = 2 × 3.14 × 18 cm
c₁ = 113.04 cm
Diameter (d₂) = 20 cm
Radius (r₂) = 20/2 cm = 10 cm
Circumference (c₂) = 2πr
c₂ = 2 × 3.14 × 10 cm
c₂ = 62.8 cm
Now,
c₁ + c₂ = Circumference (c₃)
113.04 cm + 62.8 cm = c₃
c₃ = 175.84 cm
We know the circumference of the third circle. Now, we will find the area of the third circle.
c₃ = 2πr
175.84 cm = 2 × 3.14 × r₃
175.84 cm = 6.28 × r₃
r₃ = 175.84 cm ÷ 6.28
r₃ = 28 cm
Area (a₃) = πr²
a₃ = (22/7) × (28 cm)²
a₃ = (22/7) × 28 cm × 28 cm
a₃ = 22 × 4 cm × 28 cm
a₃ = 2464 cm² or π(28 cm)²
Now, we have to find the ratio of a₃ to the sum of a₁ and a₂.
Let's find out the area of the two circles.
r₁ = 18 cm
a₁ = πr²
a₁ = π(18 cm)²
r₂ = 10 cm
a₂ = πr²
a₂ = π(10 cm)²
Now,
a₃ : a₁ + a₂
π(28²) : π(18)² + π(10)²
π(784) : π(18² + 10²)
784 ÷ 424
98 ÷ 53
98 : 53