A decorative pottery bowl with a diameter of 30 cm is used as a garden ornament . A rain shower fills it with water to a maximum depth of 7 cm. The bowl is slowly tipped to remove the water. What angle will the rim of the bowl make with the horizontal when the water begins to spill out?
Let's say the bowl is a hemisphere. Then, draw a side view. The axis of symmetry of the sphere, and the radius to the edge at the top of the bowl form a right triangle with legs 15cm long.
If the right angle is considered to be the vertex angle of an isosceles triangle, the base of the triangle is the surface of the water when it just about to start over the rim.
So, drop an altitude such that the distance from the base of the triangle to the circle of the bowl is 7cm.
Then if the bowl has been tipped an angle θ,
cosθ = 7/15.posted by Steve