$\text { Find } I _ { z } \text { for the lamina } z = x ^ { 2 } + y ^ { 2 } , 0 \leq z \leq 3 $ with uniform density of 1 Use a computer algebra system to verify your result.
A) $\frac { \pi } { 50 } ( 16 \sqrt { 16 } + 1 )$
B) $\frac { \pi } { 30 } ( 17 \sqrt { 16 } + 1 )$
C) $\frac { \pi } { 60 } \left( 17 ( 13 ) ^ { 3 / 2 } + 1 \right)$
D) $\frac { \pi } { 60 } \left( 15 ( 13 ) ^ { 3 / 2 } + 1 \right)$
E) $\frac { \pi } { 30 } \left( 16 ( 13 ) ^ { 3 / 2 } + 1 \right)$

Question

$\text { Find } I _ { z } \text { for the lamina } z = x ^ { 2 } + y ^ { 2 } , 0 \leq z \leq 3 $  with uniform density of 1   Use a  computer algebra system to verify your result. 
A) $\frac { \pi } { 50 } ( 16 \sqrt { 16 } + 1 )$
B) $\frac { \pi } { 30 } ( 17 \sqrt { 16 } + 1 )$
C) $\frac { \pi } { 60 } \left( 17 ( 13 ) ^ { 3 / 2 } + 1 \right)$
D) $\frac { \pi } { 60 } \left( 15 ( 13 ) ^ { 3 / 2 } + 1 \right)$
E) $\frac { \pi } { 30 } \left( 16 ( 13 ) ^ { 3 / 2 } + 1 \right)$

Quizplus · Accepted Answer

The moment of inertia $ I_z $ for a lamina with density 1 over the surface $ z = x^2 + y^2 $ from $ z = 0 $ to $ z = 3 $ is calculated using polar coordinates. The correct expression is $\frac { \pi } { 60 } \left( 17 ( 13 ) ^ { 3 / 2 } + 1 \right)$.

Find Iz for the lamina z=x2+y2,0≤z≤3\text { Find } I _ { z } \text { for the lamina } z = x ^ { 2 } + y ^ { 2 } , 0 \leq z \leq 3 Find Iz​ for the lamina z=x2+y2,0≤z≤3

$\text { Find } I _ { z } \text { for the lamina } z = x ^ { 2 } + y ^ { 2 } , 0 \leq z \leq 3$