BPSC 48th to 52nd Exam Prelims 2008 Solved Paper

Question : 37 of 150

Marks: +1, -0

The radius of a circle is increasing uniformly at the rate of 3 cm/sec. At what rate is the area increasing when the radius is 10 cm ?

Solution:

∵

Area of circle

π {r}^{2}

{A}=π {r}^{2}

\;{ {d} {A}}/{ {dt}}=2 π r \;{d r}/{d t} \;\; (\;{d r}/{d t}=3 {cm} {/} {sec})

⇒ \;{d A}/{ {dt}}=2 π r × 3

=2 π × 10 × 3=60 π {cm}^{2} {/} {sec}

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