Question

the volume of the ice cream cone is increasing at the rate of 10 units3/sec and its radius is increasing at the rate of 1 14 units/sec when the radius r and height h are (r, h)

Answer 1

The volume of the ice cream cone is increasing at a rate of 10 units³/sec and its radius is increasing at a rate of 1 1/4 units/sec. To find the rate of change of the height, we can use the derivative of the volume formula with respect to time.

Step-by-step explanation:

The volume of the ice cream cone can be calculated using the formula for the volume of a cone, which is V = (1/3)πr²h. The rate at which the volume is increasing is given as 10 units³/sec. Since the radius is increasing at a rate of 1 1/4 units/sec, we can use the given rate of change of the radius to find the rate of change of the height. The rate of change of the height can be found using the derivative of the volume formula with respect to time.