## Suppose that both the radius r and height h of a circular cone are increasing at a rate of 7 cm/s. How fast is the volume of the cone increa

Question

Suppose that both the radius r and height h of a circular cone are increasing at a rate of 7 cm/s. How fast is the volume of the cone increasing when r=15 cm and h=10 cm?

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1 week 2021-09-13T02:51:55+00:00 1 Answer 0

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.