1. ## Math help

I want to know how to solve such questions:

1) The radius $r$ of a cylinder is increasing at the rate of $1cm/s$ and the volume $V$ is decreasing at the rate of $1 cm^3 /s$. where $r=1$ and $h=2$, find the rates of change of:

(i) the height $h$
(ii) the surface area $S$

Note that $V=\pi r^2 h$ and $S=2\pi r^2 + 2\pi rh$

2) The region $R$ in the first quadrant is bounded by the y-axis, the line y=x and the curve $y=2- x^2$. Calculate the volume formed when R is rotated about the y-axis through 1 revolution.

(what should I do after finding the area? )

2. Hello,
Originally Posted by Musab
I want to know how to solve such questions:

1) The radius $r$ of a cylinder is increasing at the rate of $1cm/s$ and the volume $V$ is decreasing at the rate of $1 cm^3 /s$. where $r=1$ and $h=2$, find the rates of change of:

(i) the height $h$
(ii) the surface area $S$

Note that $V=\pi r^2 h$ and $S=2\pi r^2 + 2\pi rh$
Let $V(t)=\pi r^2(t) h(t)$

$V'(t)=\pi(2r(t)*r'(t)*h(t)+h'(t)r^2(t))$

Consider $r(t)=1$ and $h(t)=2$
Rate of change of the volume : V'(t)=-1 (since it decreases)
Rate of change of the radius : r'(t)=1.

(i) Solve for $h'(t)$
(ii) same reasoning, with the derivatives. Try to do it.