Answer:
V = 5858.66π
Step-by-step explanation:
This problem can be solved by using the washer method in the integration.
If you assume that the lateral of the cone is given by a line equation of the form:
[tex]z=\frac{r}{h}u[/tex]
r: radius of the cone = 26 (because for z=0 -> √( x² + y²) = 26 = r)
h: height of the cone = 26 (because for x=0 and y=0, z = 26)
you can integrate in the following form to get the volume of the cone:
[tex]V=\pi\int_0^{26}[\frac{r}{h}u]^2du=\pi\frac{r^2}{h^2}[\frac{u^3}{3}]\\\\V=\pi\frac{(26)^2}{(26)^2}\frac{(26)^3}{3}=5858.66\pi[/tex]
hence, the volume of the cone is 5858.66π
