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…

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asked Nov 17, 2019 51.4k views

2 Answers

Yegeniy · Answer 1 · 2019-11-21T00:59:32+0000

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

$V_(cylinder)=\pi r^(2)h$ (1)

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

If we divide equation (1) by
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