Calculating Surface Area by Rotating a Curve - How to Find the Surface Area?

  • Thread starter Thread starter Tranquility13
  • Start date Start date
  • Tags Tags
    Curve Rotating
AI Thread Summary
To find the surface area obtained by rotating the curve y = 1 + 4x^2 from x = 0 to x = 8 about the y-axis, one should consider dividing the area into horizontal slices. Each slice's surface area depends on its slope, which is determined by dy/dx. The next step involves calculating the surface area for these slices and then integrating over the specified range. This approach is similar to calculating volumes of revolution. Understanding surface integrals is essential for solving this problem effectively.
Tranquility13
Messages
4
Reaction score
0

Homework Statement


Find the area of the surface obtained by rotating the curve
y= 1+4 x^2
from x=0 to x = 8 about the y-axis.


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
Hi

How did you try to solve it? Or don't you know how to start?
 
Not sure how to start it.
Any assistance would be greatly appreciated.
 
Is this multidimensional calculus course?

If it is, how is surface interagrals defined?

(post in relevant HW-section in the future, this is not introductory physics)
 
Tranquility13 said:
Find the area of the surface obtained by rotating the curve
y= 1+4 x^2
from x=0 to x = 8 about the y-axis.

Hi Tranquility13! :smile:

This is like the one about volumes.

again, divide it into horizontal slices at distance y above the x-axis, with height dy (so the slope is dy/dx).

what is the surface area of this slice (remember, it depends on the slope)?

get that, and then we'll do the integral. :smile:
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Calculate the area of this pond with functions given for the perimeter
Replies
2
Views
779
Area Under Frequency versus Time Curve meaning?
Replies
8
Views
2K
Another rotation problem -- Acceleration of a ring rolling on a surface
Replies
1
Views
722
Force acting on one side of a fluid
Replies
22
Views
1K
Magnetic dipole moment and integration surfaces (Introductory Electromagnetics - Magnetistatics)
Replies
4
Views
852
System of two wheels of different sizes with an axle through their centers
2
Replies
67
Views
4K
Please explain this suggested solution for the field inside a charged hollow sphere
Replies
17
Views
1K
Show that the flywheel inside the train counteracts lean in a curve
Replies
4
Views
2K
Rotating simple harmonic oscillator
Replies
11
Views
1K
Help calculating the current from the density and a rotating frame
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top