00:01
On the basis of the information provided in the question, we are going to solve the question.
00:05
So radius of hemispair given hemispheres is equals to 5 .70 meter.
00:17
So therefore, so equation of hemispheres becomes x square plus y square plus z squared, that is equals to 20.
00:31
So this implies that z equals to square root of 25 minus x squared minus y square now to find the volume we must first draw the diagram over here so to find volume we must find the volume enclosed below by z which is equal to square root of 25 minus x square minus y square and above by plane that is z equals to 3 the intersection of plane that is z equals to 3 and hemispheres is the intersection of the equals to 3 and hemispheres is x square plus y square plus 3 plus 3 square which is equals to 25 so this implies that x square plus y square equals to 16 now the double integral is given by so double integration of square root of 25 minus x square minus y square minus 3 d y d x so let us express in polar coordinates and the limit it will become x square plus y square equals to 16 so this implies that r is equals to 4 so r lies between 0 and 4 and theta it lies between 0 and 2 pi so square root of 25 minus x square minus y square minus 3 is equals to square root of 25 minus r square minus 3.
03:01
Also, d x, d, y equals to r, dr, d theta.
03:09
So the integral, it will become volume is given by integration 0 to 2 pi, integration 0 to 4, root 25 minus r square minus 3, r, d, d theta now next triple integral triple integral that is equals to the triple integral and the limits will be x equals to c y equals to c z equals to a so here we have f d b dx, d, y, d, z...