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Anyone please HELP me How to find the volume of the solid S from: a right circular cone with height h and base radius r

Mathematics
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1/2base*height?
where base is \[pi*r^2\]
woops I was actually close The real answer is \[1/3 * pi * r^2 * h\]

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Other answers:

My first guess (which was wrong) came from my udnerstanding that a the area of a right triangle is the 1/2 base * height. I then know that the base is circular so the base will be pi*r^2 Note that ANY volume will require an area times a height.
What I try is.. as it was found that \[r = \sqrt{c ^{2}-h ^{2}}\] so the cross sectional area is A(h)= pi r^2 = pi (c^2-h^2) from the drawing.. a=0, b=h so the volume is \[\int\limits_{0}^{h} A(h) dh = \int\limits_{0}^{h} pi(c^{2}-h^{2}) dh\]
yes the answer is 1/3∗pi∗r2∗h but my explanation is false
from my previous post, when I show my work.. could you recognise which mistakes and do you hv any suggestion? thanks
Idk I haven't done multi variable cal in a while

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