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?

Respuesta :

Answer:

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.)  data:

 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              

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