Use polar coordinates to find the volume of the solid under the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ and above the disk $x ^ { 2 } + y ^ { 2 } \leq 25$.
A) $2,500 \pi$
B) $625 \pi$
C) $312.5 \pi$
D) $1,250 \pi$
E) $208.3 \pi$

Question

Quizplus · Accepted Answer

The volume is calculated using the integral in polar coordinates: $\int_{0}^{2\pi} \int_{0}^{5} (r^2) r \, dr \, d\theta$. Solving this gives $\frac{625\pi}{2} = 312.5\pi$.

Use Polar Coordinates to Find the Volume of the Solid z=x2+y2z = x ^ { 2 } + y ^ { 2 }z=x2+y2

Use Polar Coordinates to Find the Volume of the Solid $z = x ^ { 2 } + y ^ { 2 }$