Question

the volume of this triangular prism is 288 cubic centimeters. what is the value of y? y 8 cm 9 cm y = centimeters

Explanation:

Step1: Recall volume formula for triangular prism

The volume formula for a triangular prism is $V = Bh$, where $B$ is the area of the base triangle and $h$ is the height of the prism. The base triangle has base $b = 8$ cm and height $y$, so $B=\frac{1}{2}\times8\times y = 4y$. The height of the prism $h = 9$ cm. And $V=288$ $cm^{3}$.

Step2: Substitute values into the volume formula

We substitute into $V = Bh$: $288=4y\times9$.

Step3: Simplify the right - hand side

$4y\times9 = 36y$, so the equation becomes $36y=288$.

Step4: Solve for $y$

Divide both sides of the equation by 36: $y=\frac{288}{36}=8$.

Answer:

8