Math $254$ Week $10$ Recitation Activity $-$ Spring $2025$ Phee $5$ of $10$

$(7)$ Use spherical coordinates to evaluate a triple integral of $F(x,y,z)=(x^2{y}^2{x}^2{)}^{\frac{3}{2}}$ over the solid region $D,$ where $D$ is described by:

i$.$ inside the sphere of radius $5$ centered at the origin,

ii$.$ inside the cone $=\frac{}{3}$

iii. with $y0.$