Answer:
The volume of the cone is increasing at the rate oof 3848.45 cm³/s when r=15 cm and h=10 cm.
Step-by-step explanation:
The volume of the cone is given by the following formula:
In which V is measured in cm³ while r and h are measured in cm.
Suppose that both the radius r and height h of a circular cone are increasing at a rate of 7 cm/s.
This means that
How fast is the volume of the cone increasing when r=15 cm and h=10 cm?
This is when
.
Applying implicit differentiation:
We have three variables, V, r and h. So
The volume of the cone is increasing at the rate oof 3848.45 cm³/s when r=15 cm and h=10 cm.