The rate of change of the volume of the cone with respect to time in terms of r will be 78π (20r - 3r³).
The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decrease.
V = 13r² (10 − r) is the formula for calculating a cone's volume when its radius, r, and height are added together and remain constant. The radius of the cone changes at a rate of 6 with regard to time.
Differentiate the function V with respect to t. Then we have
[tex]\rm \dfrac{dV}{dt} = \dfrac{d}{dt} 13\pi r^2(10 - r)\\\\\dfrac{dV}{dt} = 13 \pi * 2r \dfrac{dr}{dt} (10-r) - 13 \pi r^2 \dfrac{dr}{dt}\\\\\dfrac{dV}{dt} = 13 \pi * 2r *6(10 - r) - 13 \pi r^2 *6\\\\\dfrac{dV}{dt} = 78 \pi (20r - 2r^2 - r^2)\\\\\dfrac{dV}{dt} = 78 \pi (20r - 3r^3)[/tex]
The rate of change of the volume of the cone with respect to time in terms of r will be 78π (20r - 3r³).
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