A stone is dropped into a quiet lake and...

A stone is dropped into a quiet lake and waves moves in circles at a speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing ?

Text Solution

Verified by Experts

The correct Answer is:

`80 pi cm^(2)//s`

Topper's Solved these Questions

APPLICATION OF DERIVATIVES
ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (LONG ANSWER TYPE QUESTIONS)|6 Videos
APPLICATION OF DERIVATIVES
ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (VERY SHORT ANSWER TYPE QUESTIONS )|12 Videos
AREA UNDER PLANE CURVES
ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (LONG ANWER TYPE QUESTIONS)|15 Videos

Similar Questions

Explore conceptually related problems

If the radius of a circle increasing from 5 cm to 5.1 cm, then find the increase area.

The radius of a circle increases at a rate of 0.2 cm/s. Calculate the rate of the increase of the area, when the radius is 5 cm.

The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing, when the side of the triangle is 20 cm ?

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference ?

The radius of a circle is increasing at the rate of 0.9 cm/s. What is the rate of increase of its circumference ?

The side of an equilateral triangle is increase at the rate of 2 cm/s. Find the rate at which the area increases, when the side of the triangle is 10 cm ?

The radius of a circle-is increasing uniformly at the rate of 3cm // s. Find the rate at which, the area of the circle is increasing, when the radius is 10 cm.

A balloon is pumped at the rate of 2 cm^3// minute. Write the rate of increase of the surface area, when the radius is 0.5 cm.

A balloon is pumped at the rate of 2 cm^3// min. .Write the rate of increase of the surface area, when the radius is 0.5 cm.

ARIHANT PUBLICATION-APPLICATION OF DERIVATIVES -CHAPTER PRACTICE (SHORT ANSWER TYPE QUESTIONS )

The side of an equilateral triangle is increasing at the rate of 2 cm/...
Text Solution
|
An edge of variable cube is increasing at the rate of 3 cm/s. How fast...
Text Solution
|
A stone is dropped into a quiet lake and waves moves in circles at a s...
Text Solution
|
The surface area of a spherical bubble is increasing at the rate of 2 ...
Text Solution
|
The volume of a spherical balloon is increasing at the rate of 25 cm^(...
Text Solution
|
A balloon which always remains sperical is being inflated by pumping i...
Text Solution
|
If the slope of the curve y = (ax)/(b-x) at the point (1, 1) is 2. The...
Text Solution
|
Find the points on the curve y = x^3 – 3x^2 + 2x at which the tangents...
Text Solution
|
Find a point on the curve f(x)=(x-3)^2, where the tangent is parallel ...
Text Solution
|
Find the points on the curve x^(2) + y^(2) - 2x - 3 = 0 at which the t...
Text Solution
|
Find the equation of tangent and normal to the ellipse (x^(2))/(a^(2))...
Text Solution
|
Find the equation of the tangent and normal to the curve 16x^(2) + 9y^...
Text Solution
|
Find the equations of tangent and normal to curve x = 1 - cos theta an...
Text Solution
|
Find the equation of the normal lines to the curve 3x^(2) - y^(2) = 8,...
Text Solution
|
Find the equations of all lines having slope -1, that are tangent to t...
Text Solution
|
Show that the line (x)/(a) + (y)/(b) = 1, touches the curve y = be^(-x...
Text Solution
|
If the straight line x cos alpha + y sin alpha = p touches the curve (...
Text Solution
|
Prove that the curves y^(2) = 4ax and xy = c^(2) cut at the right angl...
Text Solution
|
Find the intervals in which the function given by f(x) = sin 3x, x in ...
Text Solution
|
Find the intervals of the function f(x) = 4 sin^(3) x - 6 sin^(2) x + ...
Text Solution
|