# Find the volume of the solid in the first octant bounded above by z = 9 - x^2, below by z = 0 and...

## Question:

Find the volume of the solid in the first octant bounded above by {eq}\displaystyle z=9-x^2 {/eq}, below by {eq}\displaystyle z=0 {/eq} and laterally by {eq}\displaystyle y^2=3x {/eq}.

## Solving the Volume of the Region:

Solving the volume of the solid using triple integrals and the formula in setting the integral is the following {eq}\displaystyle V=\int_{x_{1}}^{x_{2}}\int_{y_{1}}^{y_{2}}\int_{z_{1}}^{z_{2}}dzdydx {/eq}. This integral, the limits of integrations are the intervals that described the given solid. The above order of integration is just one of the possible six order of integrations.

## Answer and Explanation: 1

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View this answerThe solid bounded by the surfaces is defined in the following intervals,

{eq}\displaystyle 0\leq y\leq 3,\:\frac{y^{2}}{3}\leq x\leq 3,\:0\leq z\leq...

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Chapter 11 / Lesson 9In 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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