## Related questions with answers

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.)

$f(x, y)=4 x$
$R$ : square with vertices $(0,0),(4,0),(4,4),(0,4)$

(a) $-200$
(b) $600$
(c ) $50$
(d) $125$
(e) $1000$

Solution

VerifiedThe volume of the region can be approximated as height of the region times the area of the base. Since the area in $xy$ plane is a square with the area equal to $16$ and the function $f(x,y)=4x$ is positive over the given region any negative answer can be eliminated. Next, 50 is a bit too small while 600 or 1000 is a bit too much since $4x$ does not grow that rapidly or that slowly. The most educated guess is then d), 125.

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