posted by .

Find the surface area of the part of the sphere x^2+y^2+z^2=a^2 inside the circular cylinder x^2+y^2=ay (r=a*sin(θ) in polar coordinates), with a>0.

First time posting on this website, sorry for the lack of details on my attempts but I am really not sure where to start on this problem.

A formula that is useful is A(G)=∫∫√((f_x)^2+(f_y)^2+1)dA

*f_x is the partial derivative with respect to x, f_y is the partial derivative with respect to y

I know that I need to find an equation which should be x^2+y^2+z^2=a^2, and I need to find the limits which is where I am really struggling.

Also according to my professor, I shouldn't have to use any polar coordinate conversions in order to complete this problem, which was my initial approach.

  • calculus -

    The circle in the x-y plane is

    x^2 + (y - a/2)^2 = a^2/4
    x^2 = a^2/4 - (4y^2-4ay+a^2)/4 = (y^2-ay)/4

    The limits of integration in the x-y plane are

    0 < y < a
    0 < x < (1/2)√(y^2-ay)

    then use symmetry and multiply by 4

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    We are not going to do that work for you, but will be glad to help you. The unit sphere is the sphere with radius 1 centered in the origin. They give you the coordinates of a vector. Compute the dot product of the vector and the local …
  2. Math - Calculus

    The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below. | a …
  3. Calculus

    A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible surface area of such a cylinder.
  4. geometry

    Find the surface area of each of the following a cube that is 4 cm by 4 cm by 4 cm. A right circular cylinder that is 6 cm by 12cm. A right circular prisim 8cm by 5 cm by 6 cm. A sphere that is 4cm a right circular cone that is 8cm …

    Can you check my work, please? This is for a trig study guide for my final next week. I'd like to know if I'm doing this right. :) 2. The polar coordinates of a point are given. Find the rectangular coordinates of each point. a. (5,(π
  6. Math Graph

    In polar coordinates, the graph r=sin(θ)/cos^2(θ) represents the function y=(a_n)*x^n+(a_(n−1))*x^(n−1)+…+a_0 in Cartesian coordinates, where n is a positive integer and (a_i) are real numbers. What is the value …
  7. Physics

    A sphere of radius R has inhomogeneous charge distribution on its surface. Its surface charge density is σ = σ0 cos θ, where σ0 is a positive constant, and θ is the angle from the “north pole” to the point …
  8. calculus

    Use polar coordinates to find the volume of the given solid. Inside the sphere x^2+y^2+z^2=25 and outside the cylinder x^2+y^2=1
  9. maths

    A hallow sphere has a volume of xcm^3 and a surface area of ycm^2 if the value of the diameter of the sphere is the radius of the area of a semicircle.what is the radius of a cylinder(P) if the area of the circle is equal to the area …
  10. MATH

    Find the area of the surface. The part of the paraboloid z = x2 + y2 that lies inside the cylinder x2 + y2 = 4.

More Similar Questions