Finding volume of a cone through integration

I am trying to find the volume of a cone using integration through horizontal slicing. The cone has a base radius of 10cm and a height of 5cm.

I am assuming this means I should integrate with respect to y, but I am not entirely sure how to set this up. I know that volume of a cylinder is given by the following:

$V=\pi {r}^{2}h$

So I am assuming that the integral would be:

$\pi {\int}_{0}^{5}f(y{)}^{2}dy$

I am not sure how the x value of the radius 10cm (since it is not with respect to y) should fit into the equation, though.

Also, sorry for the pseudo-code style. I do not know how to use the math typesetting yet.

I am trying to find the volume of a cone using integration through horizontal slicing. The cone has a base radius of 10cm and a height of 5cm.

I am assuming this means I should integrate with respect to y, but I am not entirely sure how to set this up. I know that volume of a cylinder is given by the following:

$V=\pi {r}^{2}h$

So I am assuming that the integral would be:

$\pi {\int}_{0}^{5}f(y{)}^{2}dy$

I am not sure how the x value of the radius 10cm (since it is not with respect to y) should fit into the equation, though.

Also, sorry for the pseudo-code style. I do not know how to use the math typesetting yet.