A cube of ice melts without changing its shape at the uniform rate of `4(c m^3)`/min The rate of change of the surface area of the cube, in `(c m^2)`/min when the volume of the cube is `125c m^3,` is (a) `-4` (b) `-(16)/5` (c) `-(16)/6` (d) `-8/(15)`

The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min . The rate of change of the volume of the cylinder, in cm^2//min , when the radius is 2c m and the height is 3cm is (a) -2pi (b) -(8pi)/5 -(3pi)/5 (d) (2pi)/5

The rate of change of the volume of a sphere w.r.t. its surface area, when the radius is 2 cm, is 1 (b) 2 (c) 3 (d) 4

The volume of a cube is increasing at the rate of 8 cm^(3) /s. How fast is the surface area increasing when the length of an edge is 12 cm?

The value of cos(1/2cos^(-1)(1/8)) is (a) 3/4 (b) -3/4 (c) 1/(16) (d) 1/4

Find the rate of change of the area of a circle with respect to its radius r when (a) r=3 cm " " (b) r=4 cm

The radius of the base of a cone is increasing at the rate of 3 cm/min and the altitude is decreasing at the rate of 4 cm/min. The rate of change of lateral surface when the radius is 7 cm and altitude is 24cm is (a) 108pic m^2//min (b) 54pic m^2//min (c) 27pic m^2//min (d) none of these

A solid cube changes its volume such that its shape remains unchanged. For such a cube of unit volume show that, rate of change of volume = (3)/(2) xx (rate of change of area of any face of the cube.).

The value of tan[cos^(-1)(4/5)+tan^(-1)(2/3)] is 6/(17) (b) 17/(6) (c) (16)/7 (d) none of these

The radius of a cylinder is increasing at the rate of 3 m/s and its altitude is decreasing at the rate of 4m/s. The rate of change of volume (m^(3)//s) when radius is 4 m and altitude 6 m is -