How to find mass of the solid S bounded by the elliptic paraboloid $z=x^2+4y^2$ and plane $z=a$ ($a>0$) if $S$ has a constant density $K$?

Question

Find the mass of the solid $S$ bounded by the elliptic paraboloid $z = x^2 + 4y^2$ and plane $z = a$ ($a > 0$) if $S$ has a constant density $K$.

Since density is constant then just find $V$ and the mass is $m=K V$. — Mhenni Benghorbal, Oct 26 '13 at 01:25
Setting up the interval is what I am having trouble with. I know the final answer should be m = (1/4)(a^2)pi. — user103284, Oct 26 '13 at 01:27

score 0 · Answer 1 · answered Oct 26 '13 at 01:51

0

Here are some steps help you to solve the problem

1) $x^2 + 4 y^2 \leq z \leq a$.

2) the region in $xy$-plane follows from the equation

$$ x^2 + 4 y^2 =a .$$

answered Oct 26 '13 at 01:51

Mhenni Benghorbal

1 Answers1