# Thread: Volume of a curve rotated around the y-axis

1. ## Volume of a curve rotated around the y-axis

Find the volume of $\displaystyle y=4-x^2$ bounded by y=0 and y=4

Is this correct?

$\displaystyle y\!:\;\;V \;=\;\pi\int^4_04-y\,.dy$

$\displaystyle V \;=\;\pi\ (4y-\frac{y^2}{2}) \bigg]^4_0$

$\displaystyle V \;=\;8\pi\ units^3$

2. yes your answer is correct. you could also use the method of cylindrical shells to find the volume

x will go from x = 0 to x = 2

the integral would be

$\displaystyle V \;=2\;\pi\int^2_0x(4-x^2)\,dx$

$\displaystyle V \;=2\;\pi\int^2_04x-x^3\,dx$

$\displaystyle V \;=2\;\pi\ (2x^2-\frac{x^4}{4}) \bigg]^2_0$

$\displaystyle V \;=2\;\pi\ (8-4)$

$\displaystyle V\;=8\;\pi$

3. Originally Posted by Dr Zoidburg
Find the volume of $\displaystyle y=4-x^2$ bounded by y=0 and y=4

Is this correct?

$\displaystyle y\!:\;\;V \;=\;\pi\int^4_04-y\,.dy$

$\displaystyle V \;=\;\pi\ (4y-\frac{y^2}{2}) \bigg]^4_0$

$\displaystyle V \;=\;8\pi\ units^3$
Yes.

4. cool.
Thanks for the confrimation.
Now onto the next question!