## Related questions with answers

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.)

$f(x, y)=15-2 y ; R$ : semicircle: $x^2+y^2=16, y \geq 0$

(a) $100$
(b) $200$
(c ) $300$
(d) $-200$
(e) $800$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Imagine this as a volume between the graph of the function $15-2y$ and semicircle. The closest rough estimation is to consider it as a volume of the half cylinder given by the semicircle as the base and $z=15$ as the top of the cylinder. The rough estimate of the given volume is

$8\pi\cdot15\approx 376$

The closest answer is $300$.

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