Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 16 - x^2...
Question:
Find 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 = 1 {/eq}.
Volume Of The Solid:
We find the volume of the solid bounded by the parabolic cylinder with the help of triple integral. In the first octant (x,y,z) passing through the origin (0,0,0).Therefore: Volume can be expressed as:
{eq}Volume= \int \int \int dz dy dx {/eq}
Answer and Explanation: 1
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View this answerAccording to the given condition we find the limits:
{eq}z = 16 - x^2 \rightarrow (1) {/eq} and the plane {eq}y = 1 {/eq}
put z = 0 , in equation...
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Volume Formulas for Pyramids, Prisms, Cones & Cylinders
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Chapter 30 / Lesson 3
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The volume inside the space of pyramids, prisms, cones, and cylinders can be calculated using specialized formulas. Learn how length, width, and height are used to calculate the volume using formulas for these four objects.
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