a cylindrical water tank has a volume of 20π cubic feet . the height of the tank is 1 foot more than 2 times of its radius . find the radius and height of the tank

pi r^2 (2r+1) = 20pi

2r^3 + r^2 - 20 = 0
r = 2
I guess you can probably figure out what h is, no?

To find the radius and height of the tank, we can set up an equation based on the given information.

Let's assume the radius of the tank is 'r'. According to the given information, the height of the tank is 1 foot more than 2 times its radius. So the height 'h' can be expressed as:

h = 2r + 1

The volume of a cylinder is given by the formula V = πr^2h. In this case, the volume V is given as 20π cubic feet. So, we can substitute these values into the equation:

20π = πr^2(2r + 1)

Now, let's solve this equation to find the value of 'r'.

Step 1: Cancel out the common factor of π on both sides:

20 = r^2(2r + 1)

Step 2: Expand the expression on the right-hand side:

20 = 2r^3 + r^2

Step 3: Rearrange the equation and set it equal to zero to solve for 'r':

2r^3 + r^2 - 20 = 0

Now we have a cubic equation that needs to be solved. We can use various methods to solve this equation, such as factoring, synthetic division, or numerical methods.

One method to solve this equation is to use the Rational Root Theorem to find a rational root (if it exists), and then use polynomial division to factorize the equation.

However, in this case, we can easily observe that 'r = 2' is a root of the equation. Thus, we can divide the cubic equation by (r - 2) using polynomial division or synthetic division to obtain a quadratic equation:

(r - 2)(2r^2 + 5r + 10) = 0

Solving the quadratic equation, we find two complex roots. Since we are dealing with physical dimensions, we disregard the complex roots.

Therefore, the radius of the tank is:

r = 2 feet

Now, we can substitute this value of 'r' back into our equation for 'h':

h = 2r + 1
h = 2(2) + 1
h = 4 + 1
h = 5 feet

Therefore, the radius of the tank is 2 feet and the height of the tank is 5 feet.