Q65 / 125 · BITSAT 2010 · Mathematics

If a circular plate is heated uniformly, its area expands \(3 c\) times as fast as its radius, then the value of \(c\) when the radius is 6 units, is

  • Correct answer
    A
    \(4 \pi\)
  • B
    \(2 \pi\)
  • C
    \(6 \pi\)
  • D
    \(3 \pi\)

Solution

Let \(A\) sq. units in the area measure when the radius is \(r\) units. their \(A=\pi r^2\) Differentiate both side w.r.t ' \(t\) ' \(\frac{d A}{d t}=2 \pi r \frac{d r}{d t}\) ...(i)) We have, \(\frac{d A}{d t}=3 c \frac{d r}{d t}\) From eqn (i), we get \(3 c \cdot \frac{d r}{d t}=2 \pi r \cdot \frac{d r}{d t} \Rightarrow 3 c=2 \pi r\) Now, \(c=\frac{2}{3} \pi(6)=4 \pi\) when \(r=6\)

Hence, the correct answer is option: 'A'.

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