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

Explanation:

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