Use cylindrical coordinates to calculate the volume above the xy-plane outside the cone z^2 = x^2 + y^2 and inside the cylinder x^2 + y^2 = 4

volume of xy-plane outside the cone = 16π/3

Step-by-step explanation:

using cylindrical coordinates

z² = x² +y² >z²=r²>z=r

x² + y² =4 >r = 2

So, the volume ∫∫∫dV equal

∫(θ = 0 to 2π) ∫(r = 0 to 2) ∫z=0 to r) 1 x (r dz dr dθ) via cylindrical coordinates

= ∫(θ = 0 to 2π) ∫(r = 0 to 2) r² dr dθ

= ∫(θ = 0 to 2π) (1/3)r³ {for r = 0 to 2} dθ

= 2π x 8/3

= 16π/3

i had a similar work too, kindly contact professor james. so far he has handled 2 online tests and a paper for me. i attained 100% in both tests and 97% on the paper. kindly let him know that i referred you, i’m johnson.

read more on -