Question

The circle A touches circle B and passes through the centre of circle B. If the area of the
circle A is 100 sq cm, then the area of circle B is
A) 200 cm B) 300 sq cm C) 400 sq cm D) 500 sq cm​

Answer 1

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.

Answer 2

Answer:

You can use ncert solutions

Step-by-step explanation: