Answer :

Given the radius of a circular plate initially is 10 cm and it increases by k%.

Let x be the radius of the circular plate, and Δx is the change in the value of x.

Hence, we have x = 10 and

Δx = 0.1k

The area of a circular plate of radius x is given by

A = πx2

On differentiating A with respect to x, we get

We know

When x = 10, we have.

Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as

Here, and Δx = 0.1k

ΔA = (20π)(0.1k)

ΔA = 2kπ

Thus, the approximate increase in the area of the circular plate is 2kπ cm2.

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