Final answer:
The volume of water in the bowl as a function of h is (2/3)π(2h - h²).
Step-by-step explanation:
The volume V of the hemispherical bowl can be calculated using the formula for the volume of a hemisphere, which is given by
V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the radius is 5 inches.
Therefore, the volume of the hemispherical bowl filled to a depth of h inches is given by
V = (2/3)π(5² - (5-h)²)
= (2/3)π(25 - (25 - 2h + h²))
= (2/3)π(2h - h²).
The special cases where h = 0 and h = 5 can be checked:
When h = 0, the volume of water in the bowl is V = (2/3)π(2(0) - (0)²) = 0.
When h = 5, the volume of water in the bowl is V = (2/3)π(2(5) - (5)²)
= (2/3)π(10 - 25)
= 10π.