3. The spherical equation phi=pi/3 is a right circular cone when graphed (pointi

Question

3.       The spherical equation phi=pi/3 is a right circular cone when graphed (pointing upward along the z-axis).

a)       Convert the given equation into rectangular coordinates. Show your work.

b)       Use calculus to show that the volume of this cone is V = pi*h3, where h is the altitude of the cone. Your work should include a double or triple integral. Use a convenient coordinate system and show all integration by hand

c)       Use calculus to find the lateral surface area of this cone with altitude h. Your work should include a double or triple integral. Use a convenient coordinate system and show all integration by hand.

please show all work and steps for a b and c

Explanation / Answer

a) x^2 +y^2 = z

b)   Volume = integration [ pi*z^2*dz]   , where z =0 to h

                     = pi*h^3/3

c) area = integration [ 2pi*z*dz]    = pi*h^2

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