



 
Hi Heather, Suppose that the thickness of the ice at time t hours is T(t) inches. The volume of a sphere is 4/3 π r^{3} so the volume of the hemisphere is 2/3 π (10 × 12)^{3} = 2/3 π 22^{3} cubic inches. The radius of the hemisphere with the ice layer at time t hours is 10 + T(t) and hence the volume of ice on the hemisphere at time t hours is
Differentiate with respect to t to arrive at an expression for V'(t) involving T(t) and T'(t). Substitute the values of T(t) and T'(t) when T(t) = 2 inches to find V'(t) at this time. If you need further help with this write back,  


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