(a) Find an expression for the volume of the small chunk

dV

shown in the figure in terms

b

(from prev. page) and the variables in the figure on this page.\

dV=b^(***)r^(**)dr**d( theta )

\ (b) Find an expression for the mass of this chunk

dm

in terms of

\\\ ho

and

dV

.\ Since

dV=

brdrd(theta)\ \ Iop view\ (c) Express the mass of the entire ring as a double integral in

r

and

\\\\theta

. (Don't forget limits)\

m=pb\\\\int_0^(2\\\\pi ) \\\\int_(R-a)^R m rd (theta)

\ (d) Evaluate the integrals to find the total mass of the ring. [Hint: first integrate over

\\\\theta

, treating

r

as a constant. Then integrate over

r

.]\

m=pb(\\\\pi )a(2R-a)

(a) Find an expression for the volume of the small chunk dV shown in the figure in terms b (from prev. page) and the variables in the figure on this page. dV=brdrd(theta) (b) Find an expression for the mass of this chunk dm in terms of and dV. Since dV=brdrd( theta) dm=pdV=dm=p(brdrd(theta) Top view (c) Express the mass of the entire ring as a double integral in r and . (Don't forget limits) (d) Evaluate the integrals to find the total mass of the ring. [Hint: first integrate over , treating r as a constant. Then integrate over r.] m=pb(pi)a(2Ra)