How to find the volume of a hemisphere on top of a cone

  • Thread starter Another
  • Start date
  • #1
97
5
upload_2018-2-10_18-27-17.png




Volume of hemi-sphere = ∫ ∫ ∫ r2 sinθ dr dθ dφ

i thing (r < r < (r + R)cosθ ) ( 0 < θ < 60 = π/6) and ( 0 < φ < 2π)

integral = 2π ∫ ⅓r3 sin θ dθ

= 2π ∫ ⅓ [((r+R)cosθ)3 - r3] sin θ dθ

i don't know how to find volume of hemi-spere
upload_2018-2-10_18-27-17.png
 

Attachments

Last edited by a moderator:

Answers and Replies

  • #2
14,137
11,436
Please do not open more than one thread with the same topic, especially if the two are both ambiguous: with or without cone, what is ##r## needed for and what is ##a## in your other thread. Furthermore, do not delete the homework template, use it! It makes reading a lot easier and if you delete it, it can be viewed as disrespectful to those who are willing to answer.

I closed the other one.
 
  • #3
97
5
Please do not open more than one thread with the same topic, especially if the two are both ambiguous: with or without cone, what is ##r## needed for and what is ##a## in your other thread. Furthermore, do not delete the homework template, use it! It makes reading a lot easier and if you delete it, it can be viewed as disrespectful to those who are willing to answer.

I closed the other one.
I'm sorry


i have problem about find volume of hemisphere on cone using triple integral. (spherical coordinates)
I do not know the true extent of r (From 0 to ??????)
 
  • #4
14,137
11,436
Beside what I've written in the other thread, with the mistakes mentioned and referring to the hemisphere without the cone involved, the final radius is ##R##. You had it almost all, beside that ##\cos \frac{\pi}{2}=0## and ##\cos 0 = 1## you only had to solve ##\int_0^R r^2dr## plus eventually the volume of the cone. I assume that it is a full hemisphere above the cone and the angle of ##30°## refers to the cone alone.
 
  • #5
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,556
767
Too bad the OP has apparently abandoned this thread. It is a half way interesting problem if done directly in untranslated spherical coordinates.
 

Related Threads on How to find the volume of a hemisphere on top of a cone

  • Last Post
Replies
10
Views
11K
Replies
17
Views
2K
Replies
1
Views
3K
Replies
1
Views
3K
Replies
1
Views
30K
Replies
5
Views
6K
Replies
3
Views
1K
  • Last Post
Replies
5
Views
4K
Replies
13
Views
4K
Replies
7
Views
11K
Top