BPSC 46th Exam Prelims 2004 Solved Paper

Question : 133 of 150

Marks: +1, -0

The area of a circle is doubled when its radius is increased by 1. The radius of the circle is-

Solution:

Area of circle

=π r^{2}

According to the question
when

{R}=r+1

, Then

2 × π r^{2}=π(r+1)^{2}

⇒ 2 π r^{2}=π(r^{2}+1+2 r)

2 r^{2}=r^{2}+1+2 r

r^{2}=\;{(r+1)^{2}}/{2}

⇒ r=√{\;{(r+1)^{2}}/{2}}=\;{r+1}/{√{2}}

⇒ √{2} r=r+1

⇒ √{2} r-r=1

⇒ r=\;{1}/{√{2}-1}

Now, dividing and multiplying by

√{2}+1

\;{1}/{√{2}-1} × \;{√{2}+1}/{√{2}+1}=\;{√{2}+1}/{√{2^{2}}-1}

=\;{√{2}+1}/{1}=√{2}+1

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