Derive the formula for the area within a circle of radius r, by dividing the region into (i) concentric circular strips of radius r'and width dr', where 0 sr's r; (ii) parallel rectangular strips lying between x and .x+d. x, where -rs. rsr. (b) derive the formula for the surface area of a sphere of radius r, by integrating out the polar and azimuthal angles in spherical coordinates (see course notes, pg 2). show that the narrow inclined circular strip lying between zand z+dz has area da = 2nrdz, where z= so a = 21rx2r (equal on the sphere and the superscribed cylinder-as was understood by archimedes.) (c) derive the formula for the volume within the sphere in (b), by dividing the region into (i) concentric spherical shells of radius r'and thickness dr', where ( sr'sr, (ii) parallel disks of thickness dz, and area a( where -psisr. charge may lie in points q, or be distributed on lines, on surface sheets, or in volumes, with densities: charge-per-unit-length a = dy/dl; charge-per-unit-area o = dq/da ; or charge-per-unit-volume p = dp/dr. these distributions can be squeezed or stretched into one another, involving mathematical infinities.