- #1
qq545282501
- 31
- 1
Homework Statement
use spherical coordinates to find the volume of the solid inside the hemisphere z= √(25-x^2-y^2) and bounded laterally by the cylinder x^2+y^2=4
Homework Equations
x=rcosθ =ρsinφcosθ , y=rsinθ =ρsinφsinθ
z=ρcosφ
r= ρsinφ
The Attempt at a Solution
I divided the solid into 2 parts, upper part is the small dome and below it is a cylinder with radius of 2 and height of sqrt(21)[ by setting z=sqrt(25-4) ]
so the volume of the cylinder = 2(r^2)h=57.59
volume of the dome= 328.98
adding the 2 volumes together give 396.87. which is greater than the volume of a hemisphere of radius 5.
so this is very wrong, but i don't know where is my mistake