A volcanic cone spews fine particles of rock which land in the surrounding area and cause the size of the cone to increase.
(a) Suppose that a volcanologist takes measurements that show that when the cone is 100 meters wide and 50 meters tall, its height is increasing at 0.5 meters/day. If the assump- tion is made that the cone will retain its height-width proportion, what is the rate at which the volume of rock is being released by the volcano? (b) Suppose that the volcanologist takes more measurements and realizes the original as- sumption was poorly made, because the radius is
increasing at 0.4 meters/day. What would be the new finding for the rate at which the volume of rock is being released by the volcano?
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