A hemispherical bowl of radius a contains water to a depth h. Find the volume of the water in the bowl. b. Water runs into a sunken concrete hemispherical bowl of radius 5 m at the rate of 0.2 m cubed divided by sec. How fast is the water level in the bowl rising when the water is 4 m deep?

a. volume = 2/3*a³

b. velocity/speed of flow = 0.00127 m/s

Step-by-step explanation:

a.) The volume of a sphere is given by 4/3πr³ where r = radius of the sphere.

The volume of the hemisphere is half the volume of the sphere = 1/2*4/3*πr³

= 2/3πr³

With a as the radius, the volume will be

v = 2/3πa³

b.) dа ta:

r = 5 m

volume flow = 0.2 m³/s

height = 4 m

Velocity is calculated by the formula:

Volume flow = area * velocity

0.2 = 2πr² * velocity

0.2/2π (5) ² = 0.00127 m/s Ans