f(y) = y^{2} g(y) = 1-y^{2}

Setting f(y) = g(y)

y^{2}=1-y^{2} --> y = ±√1/2 --> a = -√1/2 b= √1/2

Volume, V = π∫_{a}^{b}|(f(y)-d)^{2}-(g(y)-d)^{2}|dy where d = 3 in this case

V = π∫_{a}^{b}|(y^{2}-3)^{2}-(-y^{2}-2)^{2}| dy = π∫_{a}^{b}|-10y^{2}+5|dy = π(-10y^{3}/3 +5y)|_{a}^{b} = π(-5√2/3+5√2) = (10/3)√2π