Question: How many days will it take for the ice core to fully melt? Round to the nearest day. 10. An ice core (a tall circular

How many days will it take for the ice core to fully melt? Round to the nearest

day.

10. An ice core (a tall circular cylinder of ice) is taken from a glacier, where it begins to melt in the sun. Assume the rate of change of volume of ice is proportional to the surface area around the cylinder, excluding the top and bottom (which are insulated). As the ice melts its height stays constant at 2 meters and the core remains cylindrical. At time t = O the radius is initially 10 centimeters, and the volume is currently decreasing at a rate of 10 cm3 / hour. (a) (6 points) Write an initial value problem modeling the volume V(t) of the ice core over time, where V(t) is measured in cubic centimeters. Be careful with units! (b) (5 points) How many days will it take for the ice core to fully melt? Round to the nearest day

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