Question

A stone is dropped into a pond. Waves in the form of circles are generated and radius of outermost ripple increases at the rate of 5 cm/sec. Then area increased after 2 seconds is ______.

Options

• 100 π cm²/sec

• 40 cm²/sec

• 50 cm²/sec

• 25 cm²/sec

Answer 1

A stone is dropped into a pond. Waves in the form of circles are generated and radius of outermost ripple increases at the rate of 5 cm/sec. Then area increased after 2 seconds is 100 π cm²/sec.

Explanation:

We have, `"dr"/"dt"` = 5 cm/sec

A = πr² ⇒ `"dA"/"dt" = 2pi "r" "dr"/"dt"`

`=> "dA"/"dt" = 2pi(10)(5)`

= 100 π cm²/sec