Question

Let D be the solid inside the cone z = V x2 + y2, inside the sphere x2 + y2 +z? = 9 and above the plane z =1. Calculate S S SD ZdV and assign the result to q11. 12. Plot the portion of x2 + z2 = 9 above the xy-plane and between y = 1 and y = 5. Make sure you use the single figure command before plotting. Assign the result from the fsurf command to q12.

Answer 1

To calculate the triple integral ∭D Z dV, set up the limits of integration for each variable using the given solid defined by a cone, a sphere, and a plane. Then, integrate Z over the region D using the limits.

Step-by-step explanation:

To calculate the triple integral ∭D Z dV, we need to set up the limits of integration for each variable. The solid D is defined as the region inside the cone z = √(x² + y²), inside the sphere x² + y² + z² = 9, and above the plane z = 1.

First, we determine the limits of integration for x, y, and z:

• For x: from -√(9 - y² - z²) to √(9 - y² - z²)
• For y: from 1 to √(9 - z²)
• For z: from 1 to √(9 - x² - y²)

Next, we integrate Z over the region D using these limits:

∭D Z dV = ∫1⁻√(9-x²-y²) ∫1⁻√(9-z²) ∫-√(9-y²-z²)⁻√(9-y²-z²) Z dz dy dx