Answer:
The Volume of a cylinder is calculated by the following formula (equation 1):
[tex]V_{cylinder}=\pi r^{2}h[/tex] (1)
Where [tex]r[/tex] is the radius of the circle that is the base of the cylinder and [tex]h[/tex] the height.
If we divide equation (1) by [tex]h[/tex] we obtain the area of the circle, as shown in equation (2):
[tex]A_{circle}=\pi r^{2}[/tex] (2)
Now, we know the volume of the cylinder in this problem is expressed as:
[tex]V_{cylinder}=5x^{2}+15x+2[/tex] (3)
And its height as:
[tex]h=5x[/tex] (4)
Knowing this, let’s find the area of the base (area of a circle):
[tex]\frac{5x^{2}+15x+2}{5x}[/tex]
If we divide each term by the common denominator we have:
[tex]\frac{5x^{2}}{5x}+\frac{15x}{5x}+\frac{2}{5x}[/tex]
Simplifying we finally have:
[tex]x+3+\frac{2}{5x}[/tex] >>>>> This is the expression of the area of the base
