Question

Suppose that both the radius ???? and height ℎ of a circular cone are increasing at a rate of 7cm/s. How fast is the volume of the cone increasing when ????=5cm and ℎ=10cm? (Use decimal notation. Give your answer to one decimal place.)

Answer 1

Answer:

Step-by-step explanation:

$V=\frac{1}{3}r^{2}h\\\frac{dV}{dt}=\frac{1}{3}(r^{2} \frac{dh}{dt}+h*2r\frac{dr}{dt})\\\frac{dV}{dt}=\frac{1}{3}(5^{2} *7+10*2*5*7) \\\frac{dV}{dt}=\frac{1}{3}(175+700)\\\frac{dV}{dt}=\frac{1}{3}*875=291.7~cm^3$