Question

A cylindrical water tower with a radius of 11 m and a height of 50 m is filled to a height of h. The volume V of water​ (in cubic​ meters) is given by the function​ g(h) = 121pih. Determine the appropriate domain of the function. Identify the independent and dependent variables.

Answer 1

The domain of the function is 0 ≤ h ≤ 50

Independent and dependent variables are h and g respectively.

Explanation:

Given function that shows the volume of the water,

`V=121\pi h`

Where, h represents the height of water ( in meters ) filled on the water tank,

Since, the height can not be negative,

⇒ 0 ≤ h,

Also, the height of the tower is 50 m,

That is, h can not exceed 50,

⇒ h ≤ 50

By combining the inequalities,

0 ≤ h ≤ 50,

Domain of the given function is the set of all possible value of h,

Hence, Domain for the given function is 0 ≤ h ≤ 50

Now, the variable which is taken for measuring the another variable is called independent variable while the variable which is obtained by independent variable is called dependent variable,

Here, we take different values of h for finding the different values of g,

Therefore, independent and dependent variables are h and g respectively.