In this worksheet, we will practice using triple integrals in applications like the center of mass and moment of inertia of a solid with constant or variable density.

Q1:

Find the center of mass of the solid with
the given density function .

A

B

C

D

E

Q2:

Find the center of mass of the solid with
the given density function .

A

B

C

D

E

Q3:

Find the center of mass of the solid with the given density function
.

A

B

C

D

E

Q4:

Find the center of mass of the solid with the
given density function .

A

B

C

D

E

Q5:

Find the center of mass of the solid with the given
density function .

A

B

C

D

E

Q6:

Let , ,
and
be real numbers selected randomly from the interval .
What is the probability that the equation has at least one real solution for ? Rounding the value to four decimal places.

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