A) (i) is true while (ii) is false.
B) (i) is false while (ii) is true.
C) Both (i) and (ii) are true.
D) Both (i) and (ii) are false.
Correct Answer: B
Solution :
Statement (i): Radius of circle before change \[=\frac{4\pi }{2\pi }=2\] units Area of circle before change \[=\pi {{(2)}^{2}}=4\pi \,sq\] unit Radius of circle after change \[=\frac{8\pi }{2\pi }=4\] units \[\therefore \] Area of circle after change \[=\pi {{(4)}^{2}}sq\]. units. \[=16\pi \,sq\]. units Change in area \[=16\pi -4\pi =12\pi \] \[=3\times 4\pi =3\times \] original area Statement (ii): \[2\pi {{r}_{1}}=20\] and \[2\pi {{r}_{2}}=25\] Where \[{{r}_{1}}=\] radius of toy originally \[{{r}_{2}}=\] radius of toy after increase. Now, \[2\pi ({{r}_{2}}-{{r}_{1}})\,=25-20=5\] \[\Rightarrow \,\,{{r}_{2}}-{{r}_{1}}=\frac{5}{2\pi }\].
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