# Thread: Surface Area of a solid on a graph?

1. ## Surface Area of a solid on a graph?

For this question: http://i62.tinypic.com/2uh70xw.jpg I've been stuck for a while. I'm used to finding area using a cross section but is my surface area answer right? I'm not sure about it (Just for participation points, doesn't count if I get it right but I want to know if I'm doing it right) Can you take me through the steps and did I come up with the right answer?

2. ## Re: Surface Area of a solid on a graph?

I think it's similar to calculating arc length. The surface area of a small slice of width dx is $2 \pi y \sqrt {1 + (y')^2} \, dx$. You have $y = \sqrt{2x}$ and $y' = - \frac{1}{\sqrt{2x}}$. So you integrate $\int_0^2 2\pi \sqrt{2x} \sqrt{1+\frac{1}{2x}} \, dx$, which comes out to 21.322.

- Hollywood

3. ## Re: Surface Area of a solid on a graph?

Originally Posted by hollywood
I think it's similar to calculating arc length. The surface area of a small slice of width dx is $2 \pi y \sqrt {1 + (y')^2} \, dx$. You have $y = \sqrt{2x}$ and $y' = - \frac{1}{\sqrt{2x}}$. So you integrate $\int_0^2 2\pi \sqrt{2x} \sqrt{1+\frac{1}{2x}} \, dx$, which comes out to 21.322.

- Hollywood
Thank you Hollywood!