If the volume of a frustrum is given as V=πh3(R2+Rr+r2) V = π h 3 ( R 2 + R r + r 2 ) , find dVdR d V d R .

If the volume of a frustrum is given as $V=\frac{\pi h}{3}(R^2+Rr+r^2)$, find $\frac{dV}{dR}$.

Answer Details

To find dV/dR, we need to take the derivative of V with respect to R, while treating all other variables as constants. Using the product rule of differentiation, we get: dV/dR = πh/3 [2R + r] Therefore, the answer is πh/3 [2R + r]. To understand this, we need to remember that the derivative of a function gives us the rate of change of the function. In this case, the volume of a frustrum is a function of its height (h) and radii (R and r). By taking the derivative of the volume with respect to one of the radii (R), we get the rate of change of the volume with respect to that radius. In other words, dV/dR tells us how much the volume changes for a small change in R, while holding h and r constant.