The solution would be like
this for this specific problem:
V = ∫ dV
= ∫0→2 ∫
0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr
= ∫0→2 ∫
0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr
= ∫0→2 ∫
0→π/2 [ 2·r²·sin(φ) ] dφdr
= ∫0→2 [
-2·r²·cos(π/2) + 2·r²·cos(0) ] dr
= ∫0→2 [
2·r² ] dr
=
(2/3)·2³ - (2/3)·0³
= 16/3
So the volume of the
given solid is 16/3. I am hoping that these answers have satisfied
your query and it will be able to help you in your endeavors, and if you would
like, feel free to ask another question.
