Question 7

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Water is being poured into a hemispherical bowl of radius 6 inches at the rate of  .

(a) Given that the volume of the water in the spherical segment shown above is , where R is the radius of the sphere, find the rate that the water is rising when the water is 2 inches deep.

(b) Find an expression for r, the radius of the surface of the spherical segment of water in terms of h.

(c) How fast is the circular area of the surface of the spherical segment of water growing (in in²/sec) when the water is 2 inches deep?

Solution