What is the volume of the cone that has a radius of 4 inches and a slant height of 5 inches?

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Answer 1 · 2017-04-20T08:40:15

$16pi$

You can find the height using Pythagoras' theorem

![http://math.tutorvista.com/geometry/http://altitude-of-a-cone.html](https://useruploads.socratic.org/v9d1PhIqRFClTNkmrZ8Q_cone-image11.png)

$"slant height"^2= "radius"^2+"height"^2$

$"height"^2 = "slant height"^2 - "radius"^2$

$"height" = sqrt("slant height"^2 - "radius"^2)$

Plugging numbers

$"height" = sqrt(25-16)= sqrt9 = 3$

Then, plug the height into the Volume formula for Cone

$V=1/3*pi*R^2*h = 1/3*pi*16*3 = 16pi$