Learn Finding Volume with Ease: Expert Tips

Gauss-divergence theorem for volume integral of a gradient field
I need to make sure that the derivation in the book I am using is mathematically correct. The problem is about finding the volume integral of the gradient field. The author directly uses the Gauss-divergence theorem to relate the volume integral of gradient of a scalar to the surface integral of the flux through the surface surrounding this volume, i.e.
$\int_{C V}^{} \nabla ϕ d V = \int_{δ C V}^{} ϕ d S$

Addison Trujillo 2022-07-14

Finding the volume of the pyramid and also determining the increase and decrease of its volume
The volume of a pyramid with a square base x units on a side and a height of h is $V = \frac{1}{3} x^{2} h$ .
1) Suppose $x = e^{t}$ and $h = e^{- 2 t}$ . Use the chain rule to find $V^{1} (t)$ .
2) Does the volume of the pyramid increase or decrease as t increases.

Finding the volume of an object is a simple but important math skill. Whether you need to measure the capacity of a container or the size of a solid, knowing how to calculate the volume of certain shapes can help you solve many everyday tasks. Our site offers easy-to-follow tutorials on how to find the volume of different shapes, like cubes, cylinders, and cones. We also have a library of formulas and tools to help you determine the exact volume of any object. Start exploring today and learn how to find the volume of different shapes in no time!

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