Calculus

Find the length of the entire perimeter of the region inside
r = 16sin(theta) but outside r = 4.

  1. 👍 0
  2. 👎 0
  3. 👁 293
asked by Salman
  1. First define the region. Drawing a sketch chould help.

    16 sin*theta = 4 when
    theta = arcsin 1/4
    which cporresponds to 14.48 degrees and 165.52 degrees

    Your region is the area bounded by 16 sin(theta) on the outside and r = 4 on the inside. The outer curve is called a cardioid, as I recall. There is a fomula for the arc length of a cardioid at
    http://en.wikipedia.org/wiki/Cardioid

    The length of the circular arc is trivial. You will need to keep theta in radians.

    1. 👍 0
    2. 👎 0
    posted by drwls
  2. 20*(2.888912398 - .25268002551)

    1. 👍 0
    2. 👎 0
  3. 64π

    1. 👍 0
    2. 👎 0
    posted by mariel

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    Find the length of the entire perimeter of the region inside r = 16sin(theta) but outside r = 4

    asked by rao shahbaz on February 17, 2010
  2. calculus II

    Find the length of the entire perimeter of the region inside r = 11 sin (theta) but outside r = 2

    asked by Anonymous on October 23, 2010
  3. Calculus

    Find the length of the entire perimeter of the region inside r=15sin(theta) but outside r=1. I am not sure how to start the problem

    asked by Susan on December 12, 2014
  4. Calculus

    Find the length of the entire perimeter of the region inside r=5sin(theta) but outside r=1. 1=5sin(theta) theta=arcsin(1/5) r'=5cos(theta) I tried the integral between arcsin(1/5) and pi-arcsin(1/5) of

    asked by Joe on February 19, 2016
  5. Calculus

    Find the area of the region that lies inside both curves. r = (3)^(1/2) cos (theta), r = sin (theta)

    asked by Mercedes on June 9, 2010
  6. Calc 2

    Find the area of the region inside r=19sin(theta) but outside r=3

    asked by Katie on May 6, 2012
  7. math

    Two Rhombuses of the equal length and width of 10 inches each and height of 7 inches are drawn inside a quarter-circle of radius 18 inches as shown in the figure below. (a) find the perimeter of each of the Rhombuses. (b) Find the

    asked by rosland on January 10, 2009
  8. Calculus

    find the area of the region inside the limacon r= 8 + 4sin(theta) HElp!! if you can show steps, i'd be greatful

    asked by KEvin on June 2, 2014
  9. basic geometric

    10. a rectangle has width the same as a side of a square whose perimeter is 20m. the length of the rectangle is 9m. find the perimeter of this rectangle. 34. The width of a rectangular picture is one-half the length. The perimeter

    asked by vero on March 12, 2007
  10. Math/Physics

    My question is this: The potential at the surface of a sphere (radius R) is given by V_0 = k cos 3theta where k is constant. Find the potential inside and outside the sphere as well as the surface charge density (lower case

    asked by Kim on October 30, 2014

More Similar Questions