In this page question3 in application problems we are going to see solution of first question

**Question 3:**

A stone thrown into still water causes a series of concentric ripples. If the radius of outer ripple is increasing at the rate of 5 cm/sec,how fast is the area of the distributed water increasing when the outer most ripple has the radius of 12 cm/sec.

**Solution**:

Let "A" be the area and "r" be the radius

Here the radius is increasing with respect to time.

Now we need to find area increased(dA/dt) when radius = 12 cm/sec

dr/dt = 5 cm/sec

Area of circle = Π r²

A = Π r²

dA/dt = 2 Π r (dr/dt)

dA/dt = 2 Π (12) (5)

dA/dt = 24 Π (5)

dA/dt = 120 Π cm²/sec

You can also try the problems listed out below.

Questions |
Solution |

(1) The radius of a circular plate is increasing in length at 0.01 cm per second. What is the rate at which the area is increasing when the radius is 13 cm? | |

(2) A square plate is expanding uniformly each side is increasing at the constant rate of 1.5 cm/min. Find the rate at which the area is increasing when the side is 9 cm. | |

(4) The radius of a spherical balloon is increasing at the rate of 4 cm/sec. Find the rate of increases of the volume and surface area when the radius is 10 cm. | |

(5) A balloon which remains spherical is being inflated be pumping in 90 cm³/sec. Find the rate at which the surface area of the balloon is increasing when the radius is 20 cm. |