Question

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? x minus 3 StartFraction 7 x minus 9 Over x squared minus 2 EndFraction x minus 3 StartFraction 7 x minus 9 Over x cubed minus 3 x squared 5 x minus 3 EndFraction x minus 3 StartFraction 7 x 3 Over x squared minus 2 EndFraction x minus 3 StartFraction 7 x 3 Over x cubed minus 3 x squared 5 x minus 3 EndFraction.

Answer 1

To solve the problem we will put the values given to us in the formula of volume of a prism.

Prism

A prism is a 3d shape whose two sides are the base sides which are polygon, with the other faces as parallelograms.

The height of the prism is $\dfrac{(x^3-3x^2+5x-3)}{(x^2-2)}$.

Explanation

Given to us

• volume of a rectangular prism = (x3 – 3x2 5x – 3),
• area of its base = (x2 – 2)
• the volume of a rectangular prism is the product of its base area and height,

As given  to us,

$\rm{ Volume\ of\ prism = Area\ of\ base \times Height$

$\rm{ Height=\dfrac{Volume\ of\ prism}{Area\ of\ base}$

Substituting the values we get,

$\rm{ Height=\dfrac{(x^3-3x^2+5x-3)}{(x^2-2)}$

Hence, the height of the prism is $\dfrac{(x^3-3x^2+5x-3)}{(x^2-2)}$.

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