# Question2 in Application Problems

In this page question2 in application problems we are going to see solution of first question

Question 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.

Solution:

Let "a" be the side of the square and "A" be the area of the square.

Here the side is increasing with respect to time.

da/dt = 1.5 cm/min

Now we need to find the rate at which the area is increasing when the side is 9 cm. That is

we need to determine dA/dt when a = 9 cm.

Area of square = a²

A = a²

differentiate with respect to t

dA/dt = 2a (da/dt)

dA/dt = 2 (9) (1.5)

dA/dt = 18 (1.5)

dA/dt = 27 cm²/min

 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? Solution (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 (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. Solution (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. Solution

Question2 in application problems to Rate of Change 