Find the volume of the solid in the first octant bounded by the sphere \rho =16 the coordinate...
Question:
Find the volume of the solid in the first octant bounded by the sphere {eq}\rho =16 {/eq} the coordinate planes, and the cones {eq}\phi = x/6 {/eq} and {eq}\phi = x/3. {/eq}
Finding the Volume:
The objective is to find the volume of the solid by using the given equations.
The general form of volume is {eq}V = \iiint_{E} dV {/eq}
By converting into spherical coordinates, we have to find the limits for integration and get a solution.
We have to integrate the function with respect to {eq}d\rho, d\phi \ and \ d\theta {/eq}.
Answer and Explanation: 1
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View this answerThe given sphere is:
{eq}\rho = 16 {/eq}
The given cones are:
{eq}\phi = \frac{x}{3} \\ \phi = \frac{x}{6} {/eq}
Given that, it lies in first...
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Volumes of Shapes: Definition & Examples
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Chapter 11 / Lesson 9
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In this lesson, learn the definition of volume and how to find the volume of objects of various shapes. Learn from various solved volume examples.
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