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# Find the volume of the described solid $S .$A pyramid with height $h$ and rectangular base with dimensions $b$ and 2$b$

## $V=\frac{2}{3} b^{2} h$

#### Topics

Applications of Integration

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

to this my best attempt at drawing a pyramid. And if I want to find the volume of a pyramid just in general, it would be 1/3 length times with times, height length, times base, times, height and the length and the width, or what we're looking at on the base of the figure. It's that base area. And then the height is that part that is right from the base to that straight up and down portion, 90 degree angle from the base of the figure. Well, consider if instead of totally unknown, lengthen with Maybe it's like the length is twice the wit. That would mean that the length is double whatever the width is still like you'd use to be and then be in those places for length. And what? Well, then your volume do you feel in to be a your length and you fill in, be as the with or or whatever it could be whatever variable. So actually, I could combine this together and call it 2/3 B squared times H and have now a more compact formula for the volume here

Oklahoma Baptist University

#### Topics

Applications of Integration

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp