Question

The area of the base of a cylinder is found by dividing the volume of the cylinder by its height. If the volume of the cylinder is represented by 5x2 + 15x + 2 and the height is 5x, which expression represents the area of the base? x2 + 3x + 5x (5x2 + 15x + 2) x + 3 + x (x2 + 3x +2)

Answer 1

Answer:

The Volume of a cylinder is calculated by the following formula (equation 1):

$V_{cylinder}=\pi r^{2}h$     (1)

Where $r$ is the radius of the circle that is the base of the cylinder  and  $h$ the height.

If we divide equation (1) by $h$ we obtain the area of the circle, as shown in equation (2):

$A_{circle}=\pi r^{2}$     (2)

Now, we know the volume of the cylinder in this problem is expressed as:

$V_{cylinder}=5x^{2}+15x+2$     (3)

And its height as:

$h=5x$     (4)

Knowing this, let’s find the area of the base (area of a circle):

$\frac{5x^{2}+15x+2}{5x}$

If we divide each term by the common denominator we have:

$\frac{5x^{2}}{5x}+\frac{15x}{5x}+\frac{2}{5x}$

Simplifying we finally have:

$x+3+\frac{2}{5x}$  >>>>> This is the expression of the area of the base

Answer 2

The answer is x+3+2/5x