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

Question

anonymous · Answer

1/2base*height?

anonymous · Answer

where base is 
$$pi*r^2$$

anonymous · Answer

woops I was actually close The real answer is 

$$1/3 * pi * r^2 * h$$

anonymous · Answer

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.

anonymous · Answer

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
$$\int\limits_{0}^{h} A(h) dh = \int\limits_{0}^{h} pi(c^{2}-h^{2}) dh$$

anonymous · Answer

yes the answer is 1/3∗pi∗r2∗h

but my explanation is false

anonymous · Answer

from my previous post, when I show my work.. could you recognise which mistakes and do you hv any suggestion? thanks

anonymous · Answer

Idk I haven't done multi variable cal in a while