What is the volume of a right circular cylinder in terms of ‘b’ if r = 2b and h = 5b + 3?

The formula for the volume of a right circular cylinder is given by the equation:

V = πr²h

In this case, we are provided with the radius r = 2b and the height h = 5b + 3.

Now, substituting these values into the volume formula:

1. Calculate r²:

r² = (2b)² = 4b²

2. Now, substitute r² and h into the volume formula:

V = π(4b²)(5b + 3)

3. Distribute:

V = π(4b² imes 5b + 4b² imes 3)

V = π(20b³ + 12b²)

4. Finally, factor out the common term:

V = 4b²π(5b + 3)

This gives us the volume of the right circular cylinder in terms of b as:

V = 4πb²(5b + 3)