Question

Find the volume of the solid formed by the wedge of the cylinder xy created by the planes zx and zy.

a. Triple integrals are used to calculate volumes of three-dimensional solids.
b. The volume is determined by a double integral.
c. The volume cannot be calculated with triple integral.
d. The wedge of the cylinder has an undefined volume.

Answer 1

The volume of a solid formed by a wedge of a cylinder can be calculated using a triple integral, where the volume is the cross-sectional area times the height.

Step-by-step explanation:

The question involves finding the volume of a solid formed by a wedge of a cylinder, which is a common problem in calculus and can be solved by using integration. Since we are looking at a three-dimensional object, we use a triple integral to calculate the volume. Recall that the volume is the cross-sectional area A times the height h (V = Ah), and for a cylinder, the area of the circle is πr². Therefore, you can use the formula V = πr²h to find the volume of the cylinder first and then find the volume of the wedge by integrating the volume over the bounded region created by the zx and zy planes.