4. An engineer is planning a reinforced concrete ring on their computer (see picture below).The concrete ring has an inner radius r, outer radius R and height h. Such a ring hasa volume of V = Th(R² – r²). The engineer is increasing the inner radius r and theheight h by 1 m/sec at a certain time to.(a) What is the rate of change of the volume V at to if the engineer fixes R to havea constant value? (your answer should possibly involve r, R and h).(b) The engineer only has a fixed amount of concrete, so they fix V = 10500T m³. Ifr = 10 m, h = 20 m, what is the rate of change of R at to?Reinforced concrete ring - illustration.

The dimensions of the concrete ring:inner radius router radius Rheight hand the volume is given by V = πh(R2-r2) The engineer is increasing the inner radius r and height h by 1 m/sec at time t = t0.⇒drdt=1, dhdt=1 a) We want to find the rate of change of V, at t0, where R is constant. The derivative of V, with respect to t is dVdt=πh(-2r),drdt+ π(R2-r2).dhdtAt time t=t0, we are given that drdt=1, dhdt=1. Thus, rate of change of Volume at time t=t0, is given as dVdt=πh(-2r).1+ π(R2-r2).1 = πh(-2r)+ π(R2-r2)dVdt = π(R2-2rh-r2)