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Question

# Determine which value best approximates the volume of the solid between the $x y$-plane and the function over the region. (Make your selection on the basis of a sketch of the solid and not by performing any calculations.)$f(x, y)=\sqrt{x^2+y^2}$$R$ : circle bounded by $x^2+y^2=9$ $(a)$ $50$ $(b)$ $500$ $(c)$ $-500$ $(d)$ $5$ $(e)$ $5000$

Solution

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Consider a cylinder with radius of $3$ and height of $3$. Its volume is approximately a little less than twice as much as $50$ volume units. Since the solid can be considered as the two thirds of such a cylinder (i.e. the cylinder without the cone), this approximation can be appropriate. ## Recommended textbook solutions #### Thomas' Calculus

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