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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
Posted by Shahista Anjum 7 years, 1 month ago
- 2 answers
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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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
2 \( {\pi}\) r = 77
2 X 22 X r = 77 X 7
r = 49/4
r = 12.25 cm
0Thank You