Question

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 1

Answer:

$h = 3x^5-3x^2-10\text{ units}$

Step-by-step explanation:

We are given the following in the question:

Volume of cylinder =

$V=Bh$

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

Volume of cylinder =

$V = 6\pi x^7-6\pi x^4-20\pi x^2$

Base area =

$B = 2\pi x^2$

We have to find height of cylinder.

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

Thus, the height of cylinder is $3x^5-3x^2-10$ units.

Answer 2

Answer:

$h=3x^5-3x^2-10$

Step-by-step explanation:

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

We know that 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.

Let us solve for h.

$h=\frac{V}{B}$

Upon substituting our given values, we will get:

$h=\frac{6\pi x^7-6\pi x^4-20\pi x^2}{2\pi x^2}$

Let us factor out $2\pi x^2$ from numerator.

$h=\frac{2\pi x^2(3x^5-3x^2-10)}{2\pi x^2}$

Upon cancelling out same terms, we will get:

$h=3x^5-3x^2-10$

Therefore, the height of the cylinder would be $3x^5-3x^2-10$ units.