Question

the height of a right rectangular prism is three times the width of the base. the length of the base is twice the width. which expression represents the volume of the prism in terms of w, the width of the base? 5w² cubic units 6w² cubic units 5w³ cubic units 6w³ cubic units

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - prism is $V = l\times w\times h$, where $l$ is the length, $w$ is the width, and $h$ is the height.

Step2: Identify dimensions in terms of $w$

Given that the width of the base is $w$, the length of the base $l = 2w$, and the height $h = 3w$.

Step3: Substitute values into formula

Substitute $l = 2w$, $w$ (width of base) and $h = 3w$ into the volume formula $V=l\times w\times h$. So $V=(2w)\times w\times(3w)$.

Step4: Simplify the expression

$(2w)\times w\times(3w)=(2\times3)\times(w\times w\times w)=6w^{3}$.

Answer:

$6w^{3}$ cubic units