Question

00
Q.35) The circle A touches circle B and passes through the centre of circle B. If the area of the circle A
is 100 cm, then the area of circle B is​

Answer 1

Answer:

The area of circle B is 400 sq cm.

Step-by-step explanation:

We can solve this question very easily.

First we make the figure according to the question. (refer the figure)

Since, it is given that circle A touches the circle B and circle A passes through the center of circle B.

Therefore, we can understand that;

Radius \ of circle \ B = 2 \times Radius \ of circle \ A

So, r_B = 2 \ r_A

(Please refer the figure)

Now, we can write as;

Area of circle A = \pi \times (r_A)^2

100 = \dfrac{22}{7} \times (r_A)^2

(r_A)^2 = \dfrac{700}{22}

r_A = \sqrt{\dfrac{700}{22}}

Therefore, r_B = 2 \times \sqrt{\dfrac{700}{22}}

Area of circle B = \pi\left ( 2\sqrt{\dfrac{700}{22}} \right )^2

= 400 sq cm

Thus, the area of circle B is 400 sq cm.