Q. 235.0( 3 Votes )
The volume of metal in a hollow sphere is constant. If the inner radius is increasing at the rate of 1 cm/sec, find the rate of increase of the outer radius when the radii are 4 cm and 8cm respectively.
Answer :
Let the inner radius be r, outer radius be R and volume be V of a hollow sphere at any instant of time
We know the volume of the hollow sphere is
Differentiating the volume with respect to time, we get
This is the rate of the volume of the hollow sphere and it is given this is constant hence
Given that the rate of increase in inner radius of the hollow sphere,
, So the above equation becomes,
So when the radii are 4cm and 8 cm, the above equation becomes,
Therefore the rate of increase of the outer radius when the radii are 4 cm and 8cm respectively is 0.25 cm/sec
Rate this question :
Learn Rate of a Chemical Reaction65 mins
Practice Questions on Definite Integral as Limit of a Sum47 mins
Definite Integral as Limit of a Sum Means ?47 mins
Integrated Rate Equation52 mins
Factors influencing Rate of Chemical Reaction45 mins
Interactive Quiz on Integrated Rate equation58 mins
Questions Based on Factors influencing Rate of Chemical Reaction41 mins
Determining a determinant63 mins
Range of a function61 mins
Carbohydrates | A thorough Lecture39 mins
The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate if its area increasing when the side of the triangle is 20 cm?
Mathematics - Board PapersFor the curve, 
if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when 
The length x, of a rectangle, is decreasing at the rate of 5 cm/minute and the width y, is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of the area of the rectangle.
Mathematics - Board Papers