1. ## Math help

I want to know how to solve such questions:

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

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

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

2) The region $\displaystyle R$ in the first quadrant is bounded by the y-axis, the line y=x and the curve $\displaystyle y=2- x^2$. 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$\displaystyle r$ of a cylinder is increasing at the rate of $\displaystyle 1cm/s$ and the volume $\displaystyle V$ is decreasing at the rate of $\displaystyle 1 cm^3 /s$. where $\displaystyle r=1$ and $\displaystyle h=2$, find the rates of change of:

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

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

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

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

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