6 мар. 2013 г. · There are some relations between coordinates. Two of them are x=rcost,y=rsint which lead us to x2+y2=r2 relating the Cartesian and Cylindrical ...

9 мар. 2014 г. · Answer using Cylindrical Coordinates: Volume of the Shared region = Equating both the equations for z, you get z = 1/2.

20 июл. 2017 г. · I need to find the volume inside the sphere and inside the cylinder using both spherical and cylindrical coordinates.

12 февр. 2020 г. · To do the same in cylindrical coordinates, I do x→x, y→ρsinθ, z→ρcosθ. To calculate the volume, I can then do V=∫2π0∫r−rρ2(x,θ)dxdθ, where ρ(x,θ) ...

23 янв. 2021 г. · Equation of cylindrical hole: r=b. To find volume using cylindrical shell method, please take shells along the axis of the cylinder. At any ...

11 мая 2022 г. · The volume is give by V=∭EdV. where E is the solid built by above of the cone z=√x2+y2 and inside of the sphere x2+y2+z2=42.

6 мар. 2018 г. · In spherical coordinates we should have simply. V=∫2π0∫α0∫30r2sinφdrdφdθ. enter image description here.

30 авг. 2016 г. · ρ=2cosϕ⟺ρ2=2ρcosϕ⟺x2+y2+z2=2z⟺x2+y2+(z−1)2=1. So like you said, it's a sphere at (0,0,1) with r=1 and bounded by the cones ϕ=π/6 and ϕ=π/3.

27 мая 2018 г. · Find the volume of the region B bounded above by the sphere x2+y2+z2=a2 and below by the plane z=b, where a>b>0. Here I worked out z=√a2 ...

16 апр. 2021 г. · In cylindrical coordinates, the volume is. ∫2π0∫√30∫−r23−√4−r2rdrdθ=19π6. and, in spherical coordinates.