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8. [0/1 Points] DETAILS MY NOTES SCALCET9 15.3.023. PREVIOUS ANSWERS ASK YOUR TEACHER PRA We have the following. Graph Graph Description Interactive 3D Graph Help 60 50 40 30 y $x^2 + y^2 = 64$, $z = 0$ (a) Set up an iterated integral in polar coordinates for the volume of the solid under the surface and above the region D. $\int_0^{\pi/2} \int_0^8 \left( \boxed{r^2} \right) dr \, d\theta$ (b) Evaluate the iterated integral to find the volume of the solid. $\frac{1024\pi}{3}$

          8. [0/1 Points]
DETAILS
MY NOTES SCALCET9 15.3.023.
PREVIOUS ANSWERS
ASK YOUR TEACHER
PRA
We have the following.
Graph
Graph Description
Interactive 3D Graph
Help
60
50
40
30
y
$x^2 + y^2 = 64$, $z = 0$
(a) Set up an iterated integral in polar coordinates for the volume of the solid under the surface and above the region D.
$\int_0^{\pi/2} \int_0^8 \left( \boxed{r^2} \right) dr \, d\theta$
(b) Evaluate the iterated integral to find the volume of the solid.
$\frac{1024\pi}{3}$

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8. [0/1 Points]
DETAILS
MY NOTES SCALCET9 15.3.023.
PREVIOUS ANSWERS
ASK YOUR TEACHER
PRA
We have the following.
Graph
Graph Description
Interactive 3D Graph
Help
60
50
40
30
y
x^2 + y^2 = 64, z = 0
(a) Set up an iterated integral in polar coordinates for the volume of the solid under the surface and above the region D.
∫0^π/2∫0^8 ( r^2) dr dθ
(b) Evaluate the iterated integral to find the volume of the solid.
(1024π)/(3)

Added by Mariano W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Israel Hernandez

02/18/2023

Step 1

The equation of the circle is $x^2 + y^2 = 64$. In polar coordinates, this is $r^2 = 64$, so $r = 8$. The region D is described by $0 \le r \le 8$ and $0 \le \theta \le \frac{\pi}{2}$ because it's in the first quadrant. Show more…

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8. [0/1 Points] DETAILS MY NOTES SCALCET9 15.3.023. PREVIOUS ANSWERS ASK YOUR TEACHER PRA We have the following. Graph Graph Description Interactive 3D Graph Help $x^2 + y^2 = 64$, $z = 0$ (a) Set up an iterated integral in polar coordinates for the volume of the solid under the surface and above the region D. $\int_0^{\pi/2} \int_0^8$ $\boxed{r^2}$ $dr \, d\theta$ (b) Evaluate the iterated integral to find the volume of the solid. $\frac{1024\pi}{3}$

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