Practice questions of Application of derivative

1)The Radius of a circle is increasing at rate of 0.7 cm/sec.What is the rate of increase of its circumfrance..

2).The radius of a circle is increasing uniformaly ,then show that the rate of 3cm/s .Find the rate at which the area of the circle is increasing when radius is 10cm..

3)A ballon which always remains spherical ,has a variable diameter $$\frac{3}{2}(2x+1)$$ Find the rate of change of its volume with respect to x. .

4).A particle moves along a curve $$y=\frac{4}{3}x^3+5$$ . Find the points on the curve at which the y-coordinates changes as fast as the x-coordinate? .

5).A man 160 cm tall ,walks away from a source of light situated at top of a pole 6meter highat the rate of 1.1 m/sec .how fast is the lenght of his shadow increasing when he is 1 meter away from the pole?.

6).The radius of a cyclinder increases at the rate of 1 cm/sec .And its height decreases at the rate of 1 cm/sec .Find the rate of change of its volume when the radius is 5 cm and the height is 5 cm?.

7)The volume of a sphere is increasing at the rate of $8cm^3/sec$.Find the rate at which its surface area is increasing ,when the radius of sphere is 12cm?.

8).An edge of a variable cube is increasing at the rate of 3 cm /sec .How fast is its volume increasing when the edge is 10 cm long?.

9)Water is dripping out from a conical funnel at the rate of $2 cm^3/sec$ through a tiny hole at the bottom.When the slant height of water is 5 cm ,find the rate of decrease of the slant height of the curve?.

10)The lenght 'z' of a rectangle is decreasing at the rate of 3cm/sec and the width 'x' is increasing at the rate of 2cm/sec .Find the rates of cahnge of $$\text{a). PERIMETER}$$ $$b).\text{AREA OF RECTANGLE}$$ .