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? 

(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. 