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

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

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=(V)/(B)`

Upon substituting our given values, we will get:

`h=(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=(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.

Answer 2

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

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 = (V)/(B)\\\\h = (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.