Problem

Find the volume of the described solid $S .$ A t…

Question:

Problem 36 Easy Difficulty

Find the volume of the described solid $S .$
A pyramid with height $h$ and base an cquilateral triangle
with side $a($ a tetrahedron $)$

Video Answer:

Answer

$$
V=\frac{\sqrt{3}}{12} a^{2} h
$$

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Calculus 2 / BC

Essential Calculus Early Transcendentals

Chapter 7

APPLICATIONS OF INTEGRATION

Section 2

Volumes

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Video Transcript

So we have the different side views of the pyramid, the cross section. So the first thing we want to do is find the equation of the line that passes through A. B. So using point slope form, we end up getting the equation of the line is Y equals A over to H times X. So sfx the side length of the cross section is going to give us two times a over to H. X. Which is just a over a checks, plugging s into the triangle formula. We end up getting a volume equal to the interval from zero to H. Of eight times X. Dx. Which gives us um the integral from zero to H. Of route 3/4 times a over H. X squared dx. Then when we simplify this further we end up getting that. This is 3/12 3/12 A squared H. Um So that is going to be the volume in this case. And again, that's based on the side views of the pyramid, which we see her like this and like this, We see that if this is 00, the origin, then that's right. Here is point B, which is H. Over to this, right? Here is H zero. And then this right here would be H negative A over to.

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James Stewart

Essential Calculus Early Transcendentals

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Problem

Find the volume of the described solid $S .$ A t…

Answer

$$
V=\frac{\sqrt{3}}{12} a^{2} h
$$

Related Courses

Essential Calculus Early Transcendentals

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Watch More Solved Questions in Chapter 7

Video Transcript

James Stewart

Essential Calculus Early Transcendentals

Grace He

Anna Marie Vagnozzi

Samuel Hannah

Joseph Lentino

$$V=\frac{\sqrt{3}}{12} a^{2} h$$

Essential Calculus Early Transcendentals

Grace He

Anna Marie Vagnozzi

Samuel Hannah

Joseph Lentino

James StewartEssential Calculus Early Transcendentals

Grace He

Anna Marie Vagnozzi

Samuel Hannah

Joseph Lentino

$$
V=\frac{\sqrt{3}}{12} a^{2} h
$$

James Stewart

Essential Calculus Early Transcendentals