Rate of Change

[salb36]

A hemispherical bowl of radius a cm is initially full of water. The water runs out of a small hole at the bottom at a constant rate which is such that it would empty the bowl in 24 seconds. Given that, when the depth of the water is x cm the volume of water is 1/3*{Pi*x^2(3a-x ) cm^3, prove that the depth is decreasing at a rate of a^3/{36x(2a-x cm/s. Find after what time the depth of water is a/2 cm, and the rate at which the water level is then decreasing. Can anyone help me out with this prb?
TIA

 

[Deleted member 4993]

A hemispherical bowl of radius a cm is initially full of water. The water runs out of a small hole at the bottom at a constant rate which is such that it would empty the bowl in 24 seconds. Given that, when the depth of the water is x cm the volume of water is 1/3*{Pi*x^2(3a-x ) cm^3, prove that the depth is decreasing at a rate of a^3/{36x(2a-x cm/s. Find after what time the depth of water is a/2 cm, and the rate at which the water level is then decreasing. Can anyone help me out with this prb?
TIA

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Volume of a hemisphere = (2/3) * \(\displaystyle \ \pi \ * (radius)^3 \)