Question

an inverted cone has a height of 11 inches and an initial radius of 18 inches. the volume of the inverted cone is decreasing at a rate of 541 cubic inches per second, with the height being held constant. what is the rate of change of the radius, in inches per second, when the radius is 5 inches? submit an exact answer. do not forget to include a negative sign if the radius is decreasing. remember that the volume of a cone is v

Answer 1

Radius of cone is decreasing at the rate of $\frac{1623}{110\pi}$ inches

What is rate of change?

Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.

Here rate of change of radius of cone has been calculated

Radius of cone  = 18 inches

Height of cone = 11 inches

Volume of cone (V) = $\frac{1}{3} \pi r^2h$

$\frac{dV}{dt} = \frac{1}{3} \pi h (2r\frac{dr}{dt})\\-541 = \frac{2}{3} \pi \times 11\times 5\times\frac{dr}{dt}\\\frac{dr}{dt} = -\frac{541 \times 3}{2 \times \pi \times 11 \times 5}\\\frac{dr}{dt} = -\frac{1623}{110 \pi}$

Radius of cone is decreasing at the rate of $\frac{1623}{110\pi}$ inches

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