This is Calculus 1 material, rates of change (derivatives) more specifically. There are no actual values, so everything is to be done with variables, short of the numbers in the equation: V= pi*(r^2)*h. I have no idea how to start this, so please show all steps and explain, thank you.
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V= pi*(r^2)*h.
It is given r = h
hence
v = πr^3
dv/dt = 3πr^2*dr/dt
dr/dt is the rate at which the radius varies.
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It is given r = h
hence
v = πr^3
dv/dt = 3πr^2*dr/dt
dr/dt is the rate at which the radius varies.
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If the height of the cylinder is equal to the radius, then h=r. Then, the equation for the volume of a cylinder is V=(pi)(r^3). Now, taking the derivative of V with respect to the radius, the variable r, we get dV/dr=3pi(r^2)(dr/dt) by the power rule and the chain rule of differentiation. dr/dt represents the rate of change of the radius, r represents the current snapshot length of the radius as it changes and dV/dr represents how the volume changes at that moment.