Double Integration and Ellipsoid Volume
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Questions and Answers

What is the volume of the ellipsoid described by $y^2 + rac{z^2}{4} = 1$ in the first octant?

  • $3 au abc$
  • $2 au abc$
  • $4 au abc$ (correct)
  • $rac{4}{3} au abc$
  • What is the area of the circle $r = a(1+4 ext{cos} heta)$?

  • $2a(1+4 ext{cos} heta)$
  • $a^2(1+4 ext{cos} heta)$ (correct)
  • $8a(1+4 ext{cos} heta)$
  • $4a(1+4 ext{cos} heta)$
  • Find the angle between the surfaces $y^2 - z - 3 = 0$ and $y^2 + 9z = 0$ at the point $(2, -rac{1}{2})$.

  • $rac{ au}{4}$ (correct)
  • $rac{ au}{2}$
  • $rac{ au}{6}$
  • $rac{ au}{3}$
  • What is the area between the curves $y = 0$, $y = 3x-6$, and $x^2 + y^2 = 36$?

    <p>$12 au$</p> Signup and view all the answers

    Find the area enclosed by the curve $r = a(1+4 ext{cos} heta)$.

    <p>$16a^2$</p> Signup and view all the answers

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