An inverted cone is being drained of water at a rate of 30cm cubed per min. it has a height that is 4 times its radius. how fast is the radius changing when the height of the water is 6cm?

Assuming the question asks for the rate of change in the radius of the water.a diagram of the situation has been drawn.similar triangles can be used to relate. there are two different right triangles: the smaller one has sides of 6 cm and  . the other has sides of  and . these two pairs of sides share the same angle, so we can equate the ratio of those sides.the formula for the volume of a cone relates the volume of the water , the radius of the water , and the height of water .since the water follows the shape of the cone, the height of the water has to be 4 times the  radius of the water. thereforesodifferentiate both sides with respect to  (time).so plugging in the information: the radius is decreasing at a rate of  , which is approx 1.061 cm/min

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