Question

17. The ratio of area of two circles whose ratio of circumference is 3:1 will be (a) 3:1 (b) 1:3 (c)1:9 (d) 9:1​

Answer 1

Given: The ratio of circumferences of two circles is 3:1.

To find: The ratio of areas of the two circles.

Solution:

• According to the formula of circumference of a circle,

        $circumference = 2\pi r$

• Here, r is the radius of the circle.
• Hence, the ratio of circumferences of the two circles can be equated to the formula as,

        $\frac{2\pi r_{1} }{2\pi r_{2} } = \frac{3}{1}$

        $\frac{ r_{1} }{ r_{2} } = \frac{3}{1}$

• So, from here, we get the ratio of the radii of the two circled as 3:1.

• According to the formula of area of a circle,

        $area = \pi r^{2}$

• Hence, the ratio of areas of the two circles can be equated to the formula as,

        $\frac{\pi r_{1} ^{2}}{\pi r_{2} ^{2}} = (\frac{r_{1} }{r_{2} } )^{2}$

              $= (\frac{3}{1} )^{2}$

              $= \frac{9}{1}$

Therefore, the ratio of areas of the two circles is 9:1.