Answer:
- radius ≈ 18.03 cm
- depth ≈ 28.03 cm
Step-by-step explanation:
You want the radius and water depth in a spherical bowl in which the water level is 10 cm above the center of the sphere, and the circular surface has a diameter of 30 cm.
Pythagorean theorem
The geometry of the diameter of the water surface can be modeled as shown in the attachment. The radius of that surface forms one leg of a right triangle with the other leg being 10 cm. The hypotenuse of the triangle is the radius of the sphere, so we have ...
r² = 15² +10² = 325
r = √325 = 5√13 ≈ 18.03 . . . . . cm
Depth
The water depth is 10 cm more than the radius, so is ...
d = 10 +r = 10 +5√13 ≈ 28.03 . . . . . cm
The radius of the bowl is about 18.03 cm; the depth of water is about 28.03 cm.
