Question

A company makes storage tanks in the shape of a cylinder of height H and radius R. The standard model the company sells has a height of 20 cm in the radius of 20 cm. Customers may also request tanks that have a smaller radius. For each centimeter a tank’s radius decreases, however it’s height must increase by 5 cm.
The volume of a cylinder Jeckel storage tank is represented by the formula V= 3.14 (radius)^2 (height). X represent the number of centimeters by which the radius is decreased due to a customer’s request. Write a function V(x) to represent the volume of a tank a customer a request as a function of X.

Answer 1

We are given the formula for volume V:

V = 3.14 r^2 h

where r is radius and h is height

 

The standard height and radius is both 20 cm each, therefore we can write it as:

V = 3.14 (20)^2 (20)

 

It is stated that the radius can be modified, for every 1 cm change in tanks radius, the height must increase by 5 cm, therefore:

V = 3.14 (20 – x)^2 (20 + 5x)

or in general form:

V = 3.14 (r – x)^2 (h + 5x)