Determine the volume of the solid in the first octant bounded by the parabolic cylinder z = 16 -...
Question:
Determine the volume of the solid in the first octant bounded by the parabolic cylinder {eq}\; z = 16 - x^2 \; {/eq} and the plane {eq}\; y = 2 {/eq}.
Determining the Volume of the Solid:
We need to find the volume of the solid in the first octant bounded by the parabolic cylinder and the plane. The volume of the solid is,
{eq}V= \iint \ dy \ dx {/eq}
First, we need to find the region of {eq}x \ and \ y {/eq} to integrate the volume using given information.
Answer and Explanation: 1
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View this answerGiven parabolic cylinder is {eq}z = 16 - x^2 {/eq}
which is lies in the first octant, so that {eq}z=0 \\16-x^2=0 \\-x^2 = -16 \\x^2 = 16 \\ x =...
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