In this page question1 in application problems we are going to see solution of first question

**Question 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?

**Solution :**

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

rate of change = 0.01 cm

Area of circular plate A = Π r²

area of circular plate is increasing when radius increases.

Differentiate with respect to r on both sides

dA/dt = Π 2r (dr/dt)

here r = 13 cm and dr/dt = 0.01 cm

dA/dt = Π 2r (dr/dt)

dA/dt = Π 2(13) (0.01)

dA/dt = Π (26) (0.01)

dA/dt = Π (0.26)

dA/dt = 0.26 Π cm²/sec

Questions |
Solution |

(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. | |

(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. | |

(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. |