An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the lengths of the top. The prism's height is 15 , the cap's height is 8 , and the cap's radius is 9 . What is the object's volume?
1 Answer
Total volume
Explanation:
Let' consider a circumference with centre in
The intersect
Notice that
Moving to the cap's volume, it can be seen as the volume of the solid generated by the arc of circumference in the first quarter of the cartesian axis, whose explicit equation is
It results from the second theorem of Guldino that
that can be simplified as
Solved the integral we get