10th Class
Mathematics
Areas Related to Circles
Question Bank
Areas Related to Circles
question_answer
Circle \[{{C}_{2}}\] passes through the centre of circle \[{{C}_{1}}\]and is tangential to it. If the area of \[{{C}_{1}}\]is \[4\text{ }c{{m}^{2}},\] then the area of \[{{C}_{2}}\] is _____.
A) \[8\,c{{m}^{2}}\]
B) \[8\,\sqrt{\pi \,}c{{m}^{2}}\]
C) \[16\,c{{m}^{2}}\]
D) \[16\sqrt{\pi }\,c{{m}^{2}}\]
Correct Answer:
C
Solution :
Given figure is Area of \[{{C}_{1}}=4\,c{{m}^{2}}\] \[\Rightarrow \] \[4=\pi {{r}_{1}}^{2}\] \[\Rightarrow \] \[\sqrt{\frac{4}{\pi }}={{r}_{1}}\] Now, \[{{r}_{2}}=2{{r}_{1}}\] \[\Rightarrow \] \[{{r}_{2}}=\frac{2\times 2}{\sqrt{\pi }}=\frac{4}{\sqrt{\pi }}\] Area of \[{{C}_{2}}=\pi \times {{r}_{2}}^{2}=\pi \times \frac{4\times 4}{\pi }=16c{{m}^{2}}\]