Question

The areas of two circles are in the ratio 25:36.
Find the ratio of their radii​

Answer 1

Answer:

ANSWER WITH STEPS AND FULL EXPLANATION

Let the radii of the two circles be r_{1}r

1

and r_{2}r

2

respectively.

Finding the areas of the two circles

Area of the circle with radius r_{1}r

1

= \pi r_{1}^{2}πr

1

2

Area of the circle with radius r_{2}r

2

= \pi r_{2}^{2}πr

2

2

Finding the circumferences of the two circles

Circumference of the circle with radius r_{1}r

1

= 2 \pi r_{1}2πr

1

Circumference of the circle with radius r_{2}r

2

= 2 \pi r_{2}2πr

2

Now, it is given in the question that the ratio between the areas of the two circles is 25:3625:36 .

∴ \pi r_{1}^{2} : \pi r_{2}^{2} = 25:36πr

1

2

:πr

2

2

=25:36

⇒ \frac{ \pi r_{1}^{2}}{ \pi r_{2}^{2}} = \frac{25}{36}

πr

2

2

πr

1

2

=

36

25

⇒ \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{5^{2}}{6^{2}}

r

2

2

r

1

2

=

6

2

5

2

⇒ (\frac{r_{1}}{r_{2}})^{2} = (\frac{5}{6})^{2}(

r

2

r

1

)

2

=(

6

5

)

2

⇒ \frac{r_{1}}{r_{2}} = \frac{5}{6}

r

2

r

1

=

6

5

...(1)

Now, the ratio between the circumferences of the two circles should be 2 \pi r_{1} : 2 \pi r_{2}2πr

1

:2πr

2

.

Now,

2 \pi r_{1} : 2 \pi r_{2}2πr

1

:2πr

2

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

2πr

2

2πr

1

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

r

2

r

1

=\frac{5}{6}=

6

5

[ Using (1) ]

=5:6=5:6

Answer 2

Step-by-step explanation:

5:6 .................

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