Question

the volume of this triangular prism is 1,564.8 cubic meters. what is the value of v? 16.3 m 16 m v v = meters

Explanation:

Step1: Recall volume formula

The volume formula for a triangular prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height of the prism. The base is a triangle with base $b = 16$ m and height $h_{triangle}$ (which we don't need separately here as we can consider the whole - base - area relationship). The height of the prism is $h=16.3$ m. First, find the area of the triangular base $B$. Since $V = Bh$, we can re - arrange to find $B=\frac{V}{h}$.

Step2: Calculate the base area

Substitute $V = 1564.8$ m³ and $h = 16.3$ m into the formula $B=\frac{V}{h}$. So, $B=\frac{1564.8}{16.3}=96$ m².

Step3: Use base - area formula for triangle

The area of a triangle is $B=\frac{1}{2}\times base\times height$. Here, the base of the triangle is $16$ m and the height of the triangle is $v$. Since $B = 96$ m² and $B=\frac{1}{2}\times16\times v$.

Step4: Solve for $v$

We have the equation $96=\frac{1}{2}\times16\times v$. First, simplify the right - hand side: $\frac{1}{2}\times16\times v = 8v$. Then, solve for $v$ by dividing both sides of the equation $96 = 8v$ by 8. So, $v=\frac{96}{8}=12$ m.

Answer:

$12$