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The diameter of two circle are …

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The diameter of two circle are in the ratio 3:2 find the ratio of their areas find the area of the circle whose circumference is 77cm

  • 2 answers

Shweta Gulati 7 years, 1 month ago

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

\( {\pi}\) r = 77

2 X 22 X r = 77 X 7

r = 49/4

r = 12.25 cm

 

Naveen Sharma 7 years, 1 month ago

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 = \({22\over 7 } \times {49\over 4}\times {49\over 4} = 471.625 cm^2\)

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