A cylinder's volume can be calculated by the formula V=Bh, where V stands for volume, B stands for base area, and h stands for height. A certain cylinder's volume can be modeled by 6πx7−6πx4−20πx2 cubic units. If its base area is 2πx2 square units, find the cylinder's height.

Answer :

Answer:

[tex]h = 3x^5-3x^2-10\text{ units}[/tex]

Step-by-step explanation:

We are given the following in the question:

Volume of cylinder =

[tex]V=Bh[/tex]

where B is the area of base and h is the height of cylinder.

Volume of cylinder =

[tex]V = 6\pi x^7-6\pi x^4-20\pi x^2[/tex]

Base area =

[tex]B = 2\pi x^2[/tex]

We have to find height of cylinder.

[tex]h = \dfrac{V}{B}\\\\h = \dfrac{6\pi x^7-6\pi x^4-20\pi x^2}{2\pi x^2}\\\\h = 3x^5-3x^2-10\text{ units}[/tex]

Thus, the height of cylinder is [tex]3x^5-3x^2-10[/tex] units.

Answer:

[tex]h=3x^5-3x^2-10[/tex]

Step-by-step explanation:

We have been given that volume of a certain cylinder is [tex]6\pi x^7-6\pi x^4-20\pi x^2[/tex] and base area is [tex]2\pi x^2[/tex]. We are asked to find the height of the cylinder.

We know that a cylinder's volume can be calculated by the formula [tex]V=Bh[/tex], where V stands for volume, B stands for base area, and h stands for height.

Let us solve for h.

[tex]h=\frac{V}{B}[/tex]

Upon substituting our given values, we will get:

[tex]h=\frac{6\pi x^7-6\pi x^4-20\pi x^2}{2\pi x^2}[/tex]

Let us factor out [tex]2\pi x^2[/tex] from numerator.

[tex]h=\frac{2\pi x^2(3x^5-3x^2-10)}{2\pi x^2}[/tex]

Upon cancelling out same terms, we will get:

[tex]h=3x^5-3x^2-10[/tex]

Therefore, the height of the cylinder would be [tex]3x^5-3x^2-10[/tex] units.

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