The radius of a right circular cylinder is given by √(t+6) and its height is 1/6√t , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time.(Volume(V) of a cylinder with a circular base area (A) and hight (h) is given by V=Ah).

The rate change of volume of the cylinder is cubic inch per second.

Step-by-step explanation:

Given that the radius of right circular cylinder is  and its height is where t is time in second and the dimension are inches.

The base area of the cylinder is A=

Differentiating with respect to t

Differentiating with respect to t

The volume of cylinder is V= Ah

∴V= Ah

Differentiating with respect to t

The rate change of volume of the cylinder is cubic inch per second.

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5