Answer
$36.57476$
Work Step by Step
a) Given
$$x=\sqrt{\sin y}, 0 \leqslant y \leqslant \pi, \quad x=0 ; \quad \text { about } y=4$$
Since the volume of the generated solid given by
\begin{aligned}
V&=2\pi \int_a^b r(y)h(y)dy
\end{aligned}
Here
$$ h(x) =\sqrt{\sin y},\ \ r(x)= 4-y$$
Then
\begin{aligned}
V&=2\pi \int_a^b r(y)h(y)dy\\
&= 2\pi \int_{0}^{\pi} \left(4-y\right)\sqrt{\sin y}dy
\end{aligned}
b) Using the calculator, we get
\begin{aligned}
V &= 2\pi \int_{0}^{\pi} \left(4-y\right)\sqrt{\sin y}dy
\approx 36.57476
\end{aligned}
