How Do You Calculate the Volume of a Cone Using Integration?

[the_storm]

Homework Statement

Using integration, Find the Volume of a right circular cone with height h and base radius r

The Attempt at a Solution

since the volume is
V(x) = $$\int A(x) d(x)$$
so I divided the cone into horizontal circles with radius r and r = $$\sqrt{s^{2} + y^{2}}$$ where is the hypotenuse and y is the height of the cone.
then I integrate with respect to y, but I got nothing so is there any help to find the volume of the cone ?

 

[Mark44]

Homework Statement

Using integration, Find the Volume of a right circular cone with height h and base radius r

The Attempt at a Solution

since the volume is
V(x) = $$\int A(x) d(x)$$

Your integral won't look like this since you are using horizontal slices, each of width dy. The area of each slice is a function of y, not x.

so I divided the cone into horizontal circles with radius r and r = $$\sqrt{s^{2} + y^{2}}$$ where is the hypotenuse and y is the height of the cone.
then I integrate with respect to y, but I got nothing so is there any help to find the volume of the cone ?

Draw a vertical cross-section sketch of the cone, with the base on the horizontal axis and the vertex of the cone at (0, h). The cross section will be a triangle.

What is the equation of the right side of the triangle? You need to find a relationship between the radius of a slice and the height of the slice.