The region specified by - - -z-3-5-8-4-3- z- 4-5 in cylindrical coordinates has volume of

Volume in cylindrical coordinations =∫_z=3^4.5∫_ϕ=π8^π/4∫_ρ=3^5(ρ)dρ dϕ dz =∫_z=3^4.5∫_ϕ=π8^π/48. dϕ dz=∫_z=3^4.5(π)dz=1.5π =4.71 ...

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The region specified by ${(ρ, ϕ, z) : 3 \leq ρ \leq 5, \frac{π}{8} \leq ϕ \leq \frac{π}{4}, 3 \leq z \leq 4.5}$ in cylindrical coordinates has volume of
4.71

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Solution

The correct option is A 4.71
Volume in cylindrical coordinations
$= \int_{z = 3}^{4.5} \int_{ϕ = \frac{π}{8}}^{π / 4} \int_{ρ = 3}^{5} (ρ) d ρ d ϕ d z$
$= \int_{z = 3}^{4.5} \int_{ϕ = \frac{π}{8}}^{π / 4} 8. d ϕ d z = \int_{z = 3}^{4.5} (π) d z = 1.5 π = 4.71$

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The region specified by {(ρ,ϕ,z):3≤ρ≤5,π8≤ϕ≤π4,3≤z≤4.5} in cylindrical coordinates has volume of 4.71

The correct option is A 4.71Volume in cylindrical coordinations =∫4.5z=3∫π/4ϕ=π8∫5ρ=3(ρ)dρdϕdz =∫4.5z=3∫π/4ϕ=π88.dϕdz=∫4.5z=3(π)dz=1.5π=4.71

The region specified by ${(ρ, ϕ, z) : 3 \leq ρ \leq 5, \frac{π}{8} \leq ϕ \leq \frac{π}{4}, 3 \leq z \leq 4.5}$ in cylindrical coordinates has volume of
4.71

The correct option is A 4.71
Volume in cylindrical coordinations
$= \int_{z = 3}^{4.5} \int_{ϕ = \frac{π}{8}}^{π / 4} \int_{ρ = 3}^{5} (ρ) d ρ d ϕ d z$
$= \int_{z = 3}^{4.5} \int_{ϕ = \frac{π}{8}}^{π / 4} 8. d ϕ d z = \int_{z = 3}^{4.5} (π) d z = 1.5 π = 4.71$