The edge of a cube is decreasing at the rate of $0.04 \ cm/sec$. If the edge of the cube is $10 \ cm$,then the rate of decrease of the surface area of the cube is...

$A$ spherical balloon is being inflated at the rate of $35 \, cm^3/min$. The rate of increase in the surface area (in $cm^2/min$) of the balloon when its diameter is $14 \, cm$,is

Find the point on the parabola $y^2 = 18x$ where the rate of change of the $y$-coordinate is twice the rate of change of the $x$-coordinate.

$A$ spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is $1 \ cm$, the ice-cream melts at the rate of $81 \ cm^3/min$ and the thickness of the ice-cream layer decreases at the rate of $\frac{1}{4\pi} \ cm/min$. The surface area (in $cm^2$) of the chocolate ball (without the ice-cream layer) is: (in $\pi$)

Water is being filled at the rate of $1 \, cm^3/sec$ in a right circular conical vessel (vertex downwards) of height $35 \, cm$ and diameter $14 \, cm$. When the height of the water level is $10 \, cm$,the rate (in $cm^2/sec$) at which the wet conical surface area of the vessel increases is

$A$ point is moving along the curve $y^3 = 27x$. The interval in which the abscissa changes at a slower rate than the ordinate is