The base of a solid S is the region bounded by the ellipse 4x² +9y² = 36. y 4x² +9y² = 36 →x (3,0) (0, -2) Cross-sections perpendicular to the y-axis are equilateral triangles Determine the exact volume of solid S.

Q: = Find the volume of the ellipsoid x² + y² + 6z² 64.

A: Given,                x2+y2+6z2=64.

Q: 4. A 3D solid has base that sits in the x-y coordinate plane. That base is a triangle with vertices…

A: Integrating the equation of curve under certain limit gives the value of area between curve and axis…

Q: Find the center of mass of a thin plate of constant density & covering the given region. The region…

A: Density: δ The region is bounded by x=y2-2y and the line x=2y

Q: Find the center of mass of a thin plate of constant density 6 covering the given region. The region…

A:

Q: The hyperbolic paraboloid (saddle) f(x, y) = x² - y² + 4 is shown in the 3D model below. Find the…

A: Here, to find the volume f(x,y)=x2-y2+4 between the rectangle R=[-2,4]×[-1,2]

Q: The base of a solid is a square with vertices located at (1, 0),(0, 1),(−1, 0), and (0, −1). Each…

A: Given,

Q: 2 Find the volume of the ellipsoid 2y 7z 16

A: Volume of the ellipsoid for the equation,