When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.04 cm divided by min. At what rate is the plate's area increasing when the radius is 43 cm?

This question is based on implicit differentiation.Therefore, the plate's area increasing when the radius is 43 cm with the rate of 10.81.

Given:

When a circular plate of metal is heated, its radius increases at a rate of 0.04 cm divided by min.

According to the question,

As we know that, the area of a circle is given by the following formula:

It is given that, its radius increases at a rate of 0.04 cm divided by min.

Now calculating the rate at which plate's area increasing when the radius is 43 cm,

By applying implicit differentiation,

Therefore, the plate's area increasing when the radius is 43 cm with the rate of 10.81.

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The plate's area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.

Step-by-step explanation:

The area of a circle is given by the following formula:

In which the area is measured in cm².

Its radius increases at a rate of 0.04 cm divided by min.

This means that

At what rate is the plate's area increasing when the radius is 43 cm?

This is when

Applying implicit differentitation

We have two variables(A and r), so

The plate's area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.

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step-by-step explanation: