Question

A solid box is formed by placing a cylinder, having equal height and radius on top of a cube such that, the circular base of cylinder is the inscribed circle for square top of the cube. If the radius of cylinder is changing at the rate $\frac{1}{2 \pi+16} cm / s$, then the rate of change of volume of the box when radius is $2\, cm$, is (Assuming that box always remain in the given shape)

Answer 1

$\Rightarrow V=\pi r^{3}+(2 r)^{3}$
$\frac{d v}{d t}=(\pi+8) 3 r^{2} \cdot \frac{d r}{d t}$
$=(\pi+8) \cdot 3 \cdot \frac{4}{2(\pi+8)}$
$=6\, cc / \sec$