Question #8f07d

Question

Question #8f07d

1 Answer

Related questions

How do you use cylindrical shells to find the volume of a solid of revolution?
How do you find the volume of a solid of revolution using the disk method?
How do you find the volume of a solid of revolution washer method?
How do you find the volume of a cone using an integral?
How do you find the volume of the solid obtained by rotating the region bounded by $y = x$ $y=x$ and...
How do you find the volume of the solid obtained by rotating the region bounded by $y = x$ $y=x$ and...
How do I perform the following: $\int_{0}^{1} \int_{0}^{\sqrt{1 - x^{2}}} \int_{\sqrt{x^{2} + y^{2}}}^{\sqrt{2 - x^{2} - y^{2}}} x y d z d y d x$ $int_0^1int_0^sqrt(1-x^2)int_sqrt(x^2+y^2)^sqrt(2-x^2-y^2) xy dz dy dx$ ?
How do you find the volume of a region that is bounded by $x = y^{2} - 6 y + 10$ $x=y^2-6y+10$ and $x = 5$ $x=5$ and rotated...
How do you find the volume of a solid that is generated by rotating the region enclosed by the...
How do you find the volume of the solid generated by revolving the region bounded by the graph...

Impact of this question

1410 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-27T15:30:25

$V = 36 π$ $V= 36pi$

Explanation:

Consider the line:

$y = \frac{x}{4}$ $y= x/4$

For $x = 12$ $x=12$ we have $y = 3$ $y=3$ , so we can see that rotating this line around the $x$ $x$ -axis in the interval $x \in (0, 12)$ $x in (0,12)$ generates exactly the solid requested.

The element of volume generated by the cylindrical shell between $x$ $x$ and $x + d x$ $x+dx$ is given by:

$d V = π y^{2} (x) d x = π \frac{x^{2}}{16} d x$ $dV = pi y^2(x)dx = pix^2/16dx$

so, integrating over the interval:

$V = \frac{π}{16} \int_{0}^{12} x^{2} d x = \frac{π}{16} {[\frac{x^{3}}{3}]}_{0}^{12} = 36 π$ $V= pi/16 int_0^12 x^2dx = pi/16 [x^3/3]_0^12 = 36pi$

Science

Math

Humanities

... and beyond

Question #8f07d

1 Answer

Explanation:

Related questions

Impact of this question