If a circular plate is heated uniformly, its area expands 3 c times...

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 $r=6$