How do i find the volume of a pointed fifth dome?

Answer 1

OK, I looked it up to find out what a pointed fifth dome is.

I don't have time to figure it out, but I'd suggest starting with the equation of a circle centered at the origin.

Since the pointed 5th is 4/5 of a full 90 degree arc, you're going to need to figure out what the x-value of the point that is .4 pi (4/5 of pi/2) would be.

Then you would integrate to find the area under that curve.

Finally you would get the volume by integrating in a cylindrical way around the vertical x value you determined above.

I know that's a broad outline, but I hope it helps.

Answer 2

submerge it in water and use displacement