Question

A circular pIate is contracting at the uniform rate of 5cm/sec. The rate at which the perimeter is decreasing when the radius of the circle is 10 cm Jong is

Options

• \[\frac{1}{2}\] cm/sec

• \[\frac{1}{3}\] cm/sec

• \[\frac{1}{4}\] cm/sec

• none of these

Answer 1

\[\frac{1}{2}\] cm/sec

Explanation:

Let A, P and r be the area, perimeter and radius of the circle respectively at time t seconds.

Then, A = πr² and P = 2πr

A = πr² ⇒ r = `sqrt("A"/pi)`

∴ P = `2sqrt(pi"A")`

∴ `"dP"/"dt" = 2 * pi/2sqrt(pi"A") * "dA"/"dt"`

`= 1/"r" * "dA"/"dt" = 1/10 * 5 = 1/2`cm/sec