Q. 44.2( 31 Votes )
An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
Answer :
Let x be the length of a side and V be the volume of the cube, then
V = x3
…….. by chain rule
It is given that
Then, 
Thus, when x = 10cm
Then 
Therefore, the volume of the cube increasing when the edge is 10 cm long is 900 cm3/s.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
PREVIOUSThe radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.NEXTA stone is dropped into a quiet lake and waves move in circles at the 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?
RELATED QUESTIONS :
Mark the correct alternative in the following:
The radius of a circular plate is increasing at the rate of 0.01 cm/sec. The rate of increases its area when the radius is 12 cm is
RD Sharma - Volume 1
Using differentials, find the approximate values of:
Find the approximate values of 
RS Aggarwal - Mathematics
Mark the correct alternative in the following:
In a sphere the rate of change of volume is
RD Sharma - Volume 1
Using differentials, find the approximate values of:
Find the approximate values of 
RS Aggarwal - Mathematics
The total cost C (x) associated with the production of x units of an item is given by C (x) = 0.007 x3 – 0.003x2 + 15x + 4000. Find the marginal cost when 17 units are produced.
RD Sharma - Volume 1The radius of a spherical soap bubble is increasing at the rate of 0.2 cm/sec. Find the rate of increase of its surface area, when the radius is 7 cm.
RD Sharma - Volume 1