In the attachment I have arrived at the correct answer but my tutor tells me there are mistakes in the last part of my analytical method as shown in the box.
Can someone have a look and tell me whats wrong with it.
The correct answer is h=3.14m. But I do not quite understand the analatical method that you have used. Of course,
If you could please explain the analytical method that you had used to get the answer maybe I will be able to help you further.
Thanks for the reply.
Task was to find the height of a dome if the Radius was was 5.4m and volume of air space underneath = V is 160mcub
Based on the previous task...sphere cap radius = 4.6m and sphere cap height = 2.8m,the volume of air space under the dome was 104.5605811mcubed
so back to the box section of the attachment,if vol is now 160mcub then h has to be more than 2.8m,so I took initial guess at 2.9 and then trial and error and eventually got to 3.141cub= 30.98
Must be an easier way...
Of course your trial and error method is incorrect. You have got a depressed cubic equation ( ). To know how to solve it please refer The "Cubic Formula" There you would find all the necessary details about how to solve cubic equations.
Hope this helps.