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Water is flowing into a hemispherical container of radius 10cm at a constant rate of 6cm^3 per second. It is known that the formula for the volume of a solid segment cut off a sphere is V=pi/3 h^2 (3r-h), Where r is the radius of the sphere and h is the height of the segment.
a) Find the rate at which the height of the water is rising when the water height is 2cm.
b) Use Pythag to find the radius of the circular water surface when the height is h, and hence find the rate of increase of the surface area when the water height is 2cm.
Water is flowing into a hemispherical container of radius 10cm at a constant rate of 6cm^3 per second. It is known that the formula for the volume of a solid segment cut off a sphere is V=pi/3 h^2 (3r-h), Where r is the radius of the sphere and h is the height of the segment.
a) Find the rate at which the height of the water is rising when the water height is 2cm.
b) Use Pythag to find the radius of the circular water surface when the height is h, and hence find the rate of increase of the surface area when the water height is 2cm.