Question

Find the volume of a rectanglular prism if the length is x and the width is x^2 and the height is 5x^2 +4x+1. Use the formula v=l•w•h, where the l is the length, w is width and h is height, to find the volume.

Answer 1

The volume =
`5x^(5)+4x^(4)+x^(3)`

Explanation:

* The rule of the volume of the rectangular prism:

- the volume of any prism = base area × height

∵ The base of the rectangular prism is rectangle

∵ Area any rectangle = Length × Width = l × w

∴ The volume of the rectangular prism = l × w × h

* In the problem:

∵ l = x , w = x² , h = 5x² + 4x + 1

∴ The volume = (x)(x²)(5x² + 4x + 1)

* We will simplify it

- Multiply x by x² and then multiply the answer by the bracket

∵ x × x² = x³

∴ x³(5x² + 4x + 1)

∵ x³ × 5x² = 5x^5

∵ x³ × 4x = 4x^4

∵ x³ × 1 = x³

∴ The volume =
`5x^(5)+4x^(4)+x^(3)`