# Math Help - Need help with analytical method

1. ## Need help with analytical method

Hi,
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.

2. Dear manich44,

The correct answer is h=3.14m. But I do not quite understand the analatical method that you have used. Of course,

$3.14^3\neq{30.98+274.8-305.73}$

3. ## Re Analytical method

Hi,

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...
Mark..

4. Then your tutor is probably suggesting that you should explain, in your working, exactly what kind of trial and error you used.

5. Originally Posted by manich44
Hi,

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...
Mark..
Dear manich44,

Of course your trial and error method is incorrect. You have got a depressed cubic equation ( $h^3+87.48h-305.73=0$). 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.