Question

a factory makes bottled perfume. each bottle is in the shape of a triangular prism, as shown below. if the factory is filling 54 such bottles, how much perfume will the factory need (in cubic centimeters)?

Explanation:

Step1: Calculate volume of one bottle

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 length $b = 9$ cm and height of the triangle $h_{triangle}=4$ cm. The area of the base $B=\frac{1}{2}\times9\times4 = 18$ $cm^{2}$. The height of the prism $h = 6$ cm. So the volume of one bottle $V_1=18\times6=108$ $cm^{3}$.

Step2: Calculate volume for 54 bottles

If we have 54 bottles, the total volume $V = 54\times V_1$. Substitute $V_1 = 108$ $cm^{3}$ into the formula, we get $V=54\times108 = 5832$ $cm^{3}$.

Answer:

5832