The diameter of two circle are …

I guess your question has two parts:

The first part is-

Let the diameters of the two circles be 3x and 2x cms.

Area of circle in terms of diameter = $\pi \ d^2\ \over 2$

A₁ = ${ 9\pi\ x^2 \over 2}$

A₂ = ${4 \pi\ x^2 \over 2}$

A₁/A₂ = 9:4

2) The second part is:

C = ${\ 2\pi\ r}$

C = 77cm

2 ${\pi}$ r = 77

2 X 22 X r = 77 X 7

r = 49/4

r = 12.25 cm

Ans. Let the diameters of two circles are 3x and 2x.

Radius of first circle = ${3x\over 2}$

Radius of second circle = ${2x\over 2} = x$

Area of first circle = ${\pi } ({3x\over 2})^2 = {\pi 9x^2\over 4}$

Area of second circle = $\pi x^2$

=> Ratio of Areas = ${\pi 9 x^2\over 4 \pi x^2} = {9\over 4} = 9:4$

Circumference of circle = 77cm

Let Radius = r

then $2 \times {22\over 7}\times r = 77$

=> $r = { 77 \times 7 \over 2 \times 22} = {49\over 4 }$

Area of Circle = ${22\over 7 } \times {49\over 4}\times {49\over 4} = 471.625 cm^2$