Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the xaxis.
xy = 2, x = 0, y = 2, y = 4
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

Each shell has thickness dy and height x = 2/y
So, the volume v is
v = ∫[2,4] 2πrh = ∫[2,4] 2πy(2/y) dy
= ∫[2,4] 4π dy
= 8π
As a check, you can use discs, getting
v = π(4^22^2)(1/2) + ∫[1/2,1] π(R^2r^2) dx
where R=y and r=2
v = 6π + ∫[1/2,1] π((2/x)^22^2) dx
v = 6π+2π = 8π 👍
 👎
 ℹ️
 🚩
Answer this Question
Related Questions

calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y = x^8, y = 1 about the line y = 5.

calculus
1. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis 2. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = 3

Physics
A capacitor is constructed of two concentric conducting cylindrical shells. The radius of the inner cylindrical shell is 2.40 103 m, and that of the outer shell is 2.53 103 m. When the cylinders carry equal and opposite charges of magnitude 1.53 1010 C,

Calculus
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. x = 7y^2, y ≥ 0, x = 7; about y = 2

cal
Find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the xaxis.

AP calc
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 8x − x^2, y = 12; about x = 2

Calculus
Find the volume of the solid formed by rotating the region enclosed by y=e^(1x)+4 y=0 x=0 x=0.3 about the xaxis. I attempted this problem numerous time and kept on getting 5.501779941pi, using the formale integral of pi(r^2) bounded by 0.3 and 0.

Calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=π/2 about the line y=1.

Calculus
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the? Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8. 27y = x^3, y = 0,

Physics
A capacitor is constructed of two concentric conducting cylindrical shells. The radius of the inner cylindrical shell is 2.35 103 m, and that of the outer shell is 2.49 103 m. When the cylinders carry equal and opposite charges of magnitude 1.61 1010 C,

calculus 2
Find the volume of the solid formed by rotating the region enclosed by y=e^(5x) , \ y=0, \ x=0, \ x=0.8 around the yaxis Please help, i have been attempting these problems for a couple of days

calculus
Consider the solid obtained by rotating the region bounded by the given curves about the xaxis. y = 9  9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips would be greatly

Calculus
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the yaxis. y = 9e^−x^2, y = 0, x = 0, x = 1

calculus2
Use cylindrical shells to find the volume V of the solid. A sphere of radius r

Calculus
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the yaxis. y = 15e^−x^2, y = 0, x = 0, x = 1

Ap calc
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the xaxis. x + y = 3, x = 4 − (y − 1)^2

math
use the method of cylindrical shells to find the volume generated by rotation the region bounded by x=y^2+1, x=2, about y=2. Sketch the region, the solid, and a typical shell. I know that for shells, its 2pix*f(x)*dx. i am having trouble figuring out what

Calculus
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y= 2e^(−x), y= 2, x= 6; about y = 4. How exactly do you set up the integral? I know that I am supposed to use the washer method but I

Calculus
1. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = x, y = 0, y = 5, x = 6 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded

Calculus
Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y = x^3 y = 16 x about the xaxis.
Still need help?
You can ask a new question or browse existing questions.