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Can anyone help me with this question please:

Find the area of the curved surface of a right-circular cone of radius 3 and height 2 by rotating the straight line segment from (0,0) to (3,2) about the y-axis

I know the length is $\sqrt{r^2 + h^2}$ And I know we can solve it using integration but I'm not sure how

Many thanks!

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    π(length of a generatrix)×radius. That's a middle-school formula. – 2017-02-04
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    Your going to have to show thoughts, else I can almost guarantee this question will not be taken well. – 2017-02-04

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If integrals are allowed, I propose to determine the equation of this straight line in the form $x=\alpha y+\beta$ and use the formulae \begin{align*}V&=\pi\int\limits_a^b x^2\text{d}y&\text{(volume)}\\[2ex]S&=2\pi\int\limits_a^b x\sqrt{1+(x')^2}\text{d}y&\text{(surface)}\end{align*}

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    What is the x in this question? – 2017-02-04
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    The abscissa $x$ stands for a dependent variable. Please read the 1st line of my post. Try to write the equation of a straight line joining $(0,0)$ with $(3,2)$ in this form. In another words, $x$ is the abscissa, while $y$ is the ordinate. – 2017-02-04
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    So it x= 0.5 y And then take the integral from 0 to 3 of 0.5 y times sqrt( 1 + 0.5^2) ? – 2017-02-04
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    It is not $x=0.5 y$. Does $(3,2)$ fulfil this equation? – 2017-02-04
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    Oh sorry I was looking at a different question it is x=2/3 y – 2017-02-04
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    $3\ne \frac{2}{3}\cdot 2$ - be more careful. If you feel better with traditional notation then reformulate a problem to $(0,0)$ and $(2,3)$ with the rotation around $x$ axis. – 2017-02-04
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    x=3/2 y and then take the integral from 0 to 2 of 3/2y times sqrt(1+ 9/4) – 2017-02-04
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    ... multiplied by $2\pi$ for the revolution surface. – 2017-02-04
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    yeah I forgot the 2 pi. Thank you! I really appreciate it. I understand now. – 2017-02-04
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    and sorry to bother you :) – 2017-02-04