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

the answer is x+3+2/5x

Answer 2

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):

`(5x^(2)+15x+2)/(5x)`

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

`(5x^(2))/(5x)+(15x)/(5x)+(2)/(5x)`

Simplifying we finally have:

`x+3+(2)/(5x)` >>>>> This is the expression of the area of the base