kayrickard
Answered

The volume of a rectangular prism is (x3 – 3x2 + 5x – 3), and the area of its base is (x2 – 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

Verified Answer :

Answer:

The height of the prism would be \(\dfrac{x^3-3x^2+5x-3}{x^2-2}\)

Explanation:

A rectangular prism is a three dimensional shape having six rectangular shaped sides. It is also known as a cuboid.

Further Explanation:

Volume of the prism, V = \(\dfrac{x^3-3x^2+ 5x-3}\)

While, Base area, B = \(x^2-2\)

Since, for a rectangular prism,

Volume is,

\(V = B\times H\)

Where,

  • V = Volume of prism
  • H = Height of the prism
  • B = Base area of prism

By substituting the values,

\(x^3-3x^2 + 5x -3=(x^2-2)\times H\)

Divide both sides by \((x^2-2)\)

\(\dfrac{x^3-3x^2+5x-3}{x^2-2}=H\)

Hence, the height of the rectangular prism would be  \(\dfrac{x^3-3x^2+5x-3}{x^2-2}\)

Learn More:

Dimension of prism https://brainly.com/question/12399919  ( answered by Calculsita )

Keywords:

3D figures, Volume, Prism, Rectangular prism, Base area.

The volume of rectangular prism is \(x^{3}-3x^{2} +5x-3\) and the area of its base is \((x^{2} -2)\)

So, the height of the prism would be \(\frac{x^{3}-3x^{2} +5x-3 }{x^{2} -2}\)

A rectangular prism is a three dimensional shape having six rectangular shaped sides. It is also known as a cuboid.

Given:-

        Volume of the prism, \(V=x^{3} -3x^{2} +5x-3\)

         Base area, \(x^{2} -2\)

Since, for a rectangular prism,

            Volume is,

           \(V=B\)×\(H\)

Where,

  • V = Volume of prism
  • H = Height of the prism
  • B = Base area of prism          

By substituting the values,

      \(x^{3} -3x^{2} +5x-3=(x^{2} -2)\) ×\(H\)

Divide both sides by \(x^{2} -2\)

      \(\frac{x^{3}-3x^{2} +5x-3 }{x^{2} -2}=H\\\)

Hence, the height of the rectangular prism would be \(\frac{x^{3}-3x^{2} +5x-3 }{x^{2} -2}\)

For more information:-

https://brainly.com/question/20717999



Related Questions