25:81
Radius Ratio from Circumference Ratio
Let the radii of the two circles be r1 and r2, and their circumferences be C1 and C2.
The circumference formula is C = 2πr.
Given the circumference ratio:
\( \frac{C_1}{C_2} = \frac{5}{9} \)
Since the circumference (C) is directly proportional to the radius (r), the ratio of the radii is the same as the ratio of the circumferences:
\( \frac{r_1}{r_2} = \frac{C_1}{C_2} = \frac{5}{9} \)
Area Ratio Calculation
The area formula is A = πr2.
The ratio of the areas (A1 and A2) is the square of the ratio of their radii:
\( \frac{A_1}{A_2} = \frac{\pi r_1^2}{\pi r_2^2} = \left(\frac{r_1}{r_2}\right)^2 \)
Substitute the ratio of the radii (5/9) into the area formula:
\( \frac{A_1}{A_2} = \left(\frac{5}{9}\right)^2 = \frac{5^2}{9^2} = \frac{25}{81} \)
Therefore, the ratio of the areas of the two circles is 25:81.
Important Questions from Circles
If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
What is the area of minor segment ?
What is the area of major segment ?
A straight line x = y + 2 touches the circle 4(x 2+ y 2) = r 2. The value of r is
If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are
