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.