A pond has the shape of an ice cream cone with the tip slices off and has a depth of 5.00m. The atmospheric pressure above the pond is 1.01 *10^5 Pa. The circular top surface (radius = R2) and circular bottum (radis = R1) of the pond are both parrallel to the ground. The angle between the ground and the side of the pond is 60 degrees. The magnitude of the force acting on the top surface is the same as the magnitude of the force acting on the bottum surface. Calculate R1 and R2.

Question

Help please, I am currently manipulating formulas, but this seems extremely complicated, can someone show me the process to which they got the answer and I will compare it with my way. Thanks.

Answer 1

You need to solve two simultaneous equations for R1 and R2.

The first is the geometrical relation:
R2 = R1 + 5/tan 60 = R1 + 2.89 m

The second is the physics relation:

pi*R2^2 * Po =
pi*R1^2 (Po + rho*g*depth)

Po = atmospheric pressure = 1.01*10^5 Pa
rho*g*depth = 0.49*10^5 Pa
R2^2/R1^2 = 1.50/1.01 = 1.49
R2/R1 = 1.22

Take it from there.

Answer 2

o wow, i didn't even think of the geometrical way, thanks.