Question

Solid of Revolution Consider the following integral, which calculates the volume of a cylinder by considering it as a solid of revolution: ∫2π0dϕ∫R0drhorhoh, where h is the height, rho is the integration variable of the radius from 0 to R, and ϕ is the integration variable of the angle from 0 to 2π. Solve this integral symbolically. Store your result in a variable volume, which should be a sympy expression. Use the variables names phi for

Answer 1

Answer:

Step-by-step explanation:

In this case the solution of the integral is

$\int\limits^{2\pi} _0 {} \, d\phi \int\limits^R_0 {\rho}h \, d\rho = [2\pi - 0](\frac{1}{2} )[R^{2} - 0]h = \pi R^{2}h$

because h is a constant, and where the expression

$\int {\rho} \, d\rho = \frac{\rho^{2}}{2}$

was used.

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