Gravel is poured into a conical pile. As more gravel is poured in, the volume, V,...

 

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Gravel is poured into a conical pile. As more gravel is poured in, the volume, V, of the pile changes with time. As a result, the height h and the radius r of the pile also change with time. Given that V = ar?h, the relationship between the changes with respect to time in the volume V(t), the radius r(t), and the height h(t) is given by: %3D (Hint: take the derivative of the volume formula using implicit differentiation, chain rule, and product rule.) Select one: dV(t) O a. = 0 dt dV(t) Ob. dt dr(t) *2r(t)- + h(t) dt dV (t) dh(t) *(2r(t) + dt %3D dt dV (t) d. 1. (2r(0) h(e) + r(1) dr(t) r(t). dt dh(t) (t) dt Check Gravel is poured into a conical pile. As more gravel is poured in, the volume, V, of the pile changes with time. As a result, the height h and the radius r of the pile also change with time. Given that V = ar?h, the relationship between the changes with respect to time in the volume V(t), the radius r(t), and the height h(t) is given by: %3D (Hint: take the derivative of the volume formula using implicit differentiation, chain rule, and product rule.) Select one: dV(t) O a. = 0 dt dV(t) Ob. dt dr(t) *2r(t)- + h(t) dt dV (t) dh(t) *(2r(t) + dt %3D dt dV (t) d. 1. (2r(0) h(e) + r(1) dr(t) r(t). dt dh(t) (t) dt Check