Find the volume V of the described solid S. A cap of a sphere with radius r and height h. V=? 12110601451.jpg

Elleanor Mckenzie

Elleanor Mckenzie

Answered question

2021-05-30

Find the volume V of the described solid S.
A cap of a sphere with radius r and height h.
V=?

Answer & Explanation

doplovif

doplovif

Skilled2021-05-31Added 71 answers

Solution:
Let
r = radius of sphere
h = height of cap
x2=r2y2
Integrate from y = r-h to y = r
Volume = πx2dy=π(r2y2)dy
=πr2yπy33 | [Evaluated from r-h to r]
=(πr3πr33)[πr2(rh)π(rh)33]
=2πr33πr3+πr2h+(π3)(r33r2h+3rh2h3)
=πr33+πr2h+(πr33πr2h+πrh2πh33)
=(πh23)(3rh)

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