The volume of an object expressed in spherical coordinates

The volume of an object expressed in spherical coordinates is given by

The value of the integral is

V =

r² sinφ drdφdθ

=			r³		¹	sinφ dφdθ
			3		₀

=		1	sinφ dφdθ
		3

=	1		[ - cosφ ]	^{π / 3}	dθ
	3			₀

=	1		1	dθ =	1	× 2π =	π
	3		2		6		3