Speed of the traveling ripple outward is  cm/sec.

.

Consider the ripple covers  cm in  seconds.

Substitute corresponding values in distance formula.

Differentiate on each side with respect to  .

Area of the circular ripple is  , Where  is its radius.

.

Differentiate on each side with respect to  .

.

Substitute  and  in above expression.

(a)

Rate at which the area of the circle is increasing after  sec:

.

Substitute  in above expression.

.

 cm²/sec.

(b)

Rate at which the area of the circle is increasing after  sec:

.

Substitute  in above expression.

 cm²/sec.

(c)

Rate at which the area of the circle is increasing after  sec:

Substitute  in above expression.

 cm²/sec.

Conclusion :

Area of the ripple increases as the time increases.

(a)  cm²/sec.

(b)  cm²/sec.

(c)  cm²/sec.

Area of the ripple increases as the time increases.