# Worksheet: Triple Integrals

In this worksheet, we will practice solving triple integration problems as well as applications of triple integration.

Q1:

Evaluate the triple integral .

Q2:

Evaluate the triple integral .

Q3:

Evaluate the triple integral .

• A
• B
• C
• D
• E

Q4:

Evaluate the triple integral .

• A1
• B
• C
• D
• E

Q5:

Evaluate the triple integral .

• A
• B
• C
• D
• E

Q6:

Evaluate the triple integral .

• A
• B
• C
• D
• E

Q7:

Evaluate the triple integral .

• A
• B
• C
• D
• E

Q8:

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

• A
• B
• C
• D
• E

Q9:

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

• A
• B
• C
• D
• E

Q10:

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

• A
• B
• C
• D
• E

Q11:

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

• A
• B
• C
• D
• E

Q12:

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

• A
• B
• C
• D
• E

Q13:

Evaluate the triple integral .

• A1
• B
• C
• D
• E

Q14:

Find the volume inside the cone , where .

• A
• B
• C
• D
• E

Q15:

Find the volume inside the cone , where .

• A
• B
• C
• D
• E

Q16:

Find the volume inside the elliptic cylinder , where .

• A
• B
• C
• D
• E

Q17:

Find, in terms of , the volume of the region that lies within both the sphere with equation and the cylinder with equation .

• A
• B
• C
• D
• E

Q18:

Find the volume inside both the sphere and the cone .

• A
• B
• C
• D
• E

Q19:

Find the volume of the solid bounded by the three coordinate planes and the plane .

Q20:

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.