An opaque cylindrical tank with an open top has a diameter of 3.25 m and is completely filled with water. When the afternoon Sun reaches an angle of 22.8° above the horizon, sunlight ceases to illuminate the bottom of the tank. How deep is the tank

10.69

Step-by-step explanation:

We must first know that the angle of refraction is given by the following equation:

n_water * sin (A_water) = n_air * sin (A_air)

where n is the refractive index, for water it is 1.33 and for air it is 1.

The angle (A) in the air is 22.8 °, and that of the water is unknown.

Replacing these values we have to:

1.33 * sin (A_water) = 1 * 0.387

sin (A_water) = 1 * 0.387 / 1.33

A_water = arc sin (0.2907) = 16.9 °

now for the tank depth:

h = D / tan (A_water)

D = 3.25

Replacing

h = 3.25 / tan 16.9 °

h = 10.69

Therefore the depth is 10.69 meters.

Doubling in size,

if the whole dish is filled in an hour (all of it)
how long does it take to fill 1/2 dish?

notice that
1/2 doubled=1/2 times 2=2/2=1 whole dish
therefor it only doubled one more time from the 1/2 point

1hour=all
1hour-6mins=1/2 dish

1hour-6mins=60-6=54 minutes

answer is 54 minutes