Question

43. The diameter of two circles are 36 cm and 20 cm respective -- Piese area of the c
which has circumference equal to the sum of the circunferences of the two circles.
find ratio of area of this big circle and the sum of area of two s nalí eszcie.
10​

Answer 1

Answer:

Area = π(784) = 2464 cm²

Ratio = 98 : 53

Step-by-step explanation:

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 + circumference of 2nd circle.

=> 2π(18) + 2π(10) = 2πR

=> 2π[18 + 10] = 2πR

=> 18 + 10 = R

=> 28 = R

Area of biggest circle= πR² = π(28)² = 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

Answer 2

$\large \mathfrak{ Given}$

Diameter = 36 cm and 20 cm

$\large \mathfrak {To \: Find}$

Ratio of area

$\large \mathfrak{Solution}$

At first

Radius = 36/2

Radius = 18 cm

Radius = 20/2

Radius = 10 cm

Now

Circumference = 2πr

2πr + 2πr' = 2πR

2π(r + r') = 2πR

2π(18 + 10) = 2πR

2π(28) = 2πR

28 = R

So

Radius = 28 cm

Area = πr²

Area = 22/7 × 28 × 28

Area = 352 cm²

Now

Sum of Areas = π(18² + 10²)

Sum of Areas = π(324 + 100)

Sum of Areas = π(424)

Now

Ratio = π784/π424

Ratio = 784/424

Ratio = 98/53