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The volume V of a circular cone is given by the formula $V=\frac{1}{3} \pi r^{2} h,$ where $r$ is the radius of the base and $h$ is the height. What is the volume of the cone in terms of $b ?$

$V=32 \pi b^{4}$

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Missouri State University

Campbell University

McMaster University

University of Michigan - Ann Arbor

this problem were given the formula for volume of a cone. It's 1/3 pi r squared H and we're as to find the volume of that cone, given its its radius and height. Okay, so 1/3 pie, the radius of that cone is to be squared, and the radius gets swears A to B squared, squared, radius squared radius is to be squared, and we're in a square times the height, which is 24. Okay, so to simplify this, the first thing we're gonna need to do is square the radius. So to be squared squared is ah, four B to the fourth. So you score the two that's four and just scored the B square. That's beat of the fourth. Now we need to simplify this expression. We can combine a lot of things together. The first thing I would do is get rid of this 1/3 1 3rd of 24 is eight. So that'll clean things up a lot. And now we can go with one times four times eight is 32 times the pie times the beat of the fourth. So 32 pi beat of the fourth is the volume of this. Come