Problem 1 Consider a sphere of radius R. In the spherical polar coordinate if we choose aparticular value for any coordinate, it gives a surface. Two such surfaces can form an envelop whichenclose a volume. Find the surface area/volume enclosed by envelopes with θ = 0◦ and 30◦, θ = 30◦to60◦. Repeat the same exercise for envelopes with same azimuthal angle separation ie., φ = 0◦to 30◦and φ = 30◦to 60◦. Compare the area/volume you get in different cases. Sketch the envelopes. Problem 1Consider a sphere of radius R. In the spherical polar coordinate if we choose aparticular value for any coordinate, it gives a surface. Two such surfaces can form an envelop whichenclose a volume. Find the surface area/volume enclosed by envelopes with 0 = 0° and 30°, 0 = 30° to60°. Repeat the same exercise for envelopes with same azimuthal angle separation ie., o = 0° to 30°and o = 30° to 60°. Compare the area/volume you get in different cases. Sketch the envelopes.

The small volume element dV and surface element (perpendicular to radius) dS in the spherical polar…

Consider a sphere of radius R. In the spherical polar coordinate if we choose a particular value for any coordinate, it gives a surface. Two such surfaces can form an envelop which enclose a volume. Find the surface area/volume enclosed by envelopes with θ = 0◦ and 30◦ , θ = 30◦ to 60◦ . Repeat the same exercise for envelopes with same azimuthal angle separation ie., φ = 0◦ to 30◦ and φ = 30◦ to 60◦ . Compare the area/volume you get in different cases. Sketch the envelopes.

Consider a sphere of radius R. In the spherical polar coordinate if we choose a particular value for any coordinate, it gives a surface. Two such surfaces can form an envelop which enclose a volume. Find the surface area/volume enclosed by envelopes with θ = 0◦ and 30◦ , θ = 30◦ to 60◦ . Repeat the same exercise for envelopes with same azimuthal angle separation ie., φ = 0◦ to 30◦ and φ = 30◦ to 60◦ . Compare the area/volume you get in different cases. Sketch the envelopes.