Question

a factory makes bottled cologne. each bottle is in the shape of a triangular prism, as shown below. if the factory used 4800 cm³ of cologne, how many bottles did the factory fill with cologne?

Explanation:

Step1: Calculate the volume of one bottle

The volume \(V\) of a triangular prism is given by \(V = \text{Base Area}\times\text{Height}\). The base of the triangular prism is a triangle with base \(b = 6\space cm\) and height \(h = 5\space cm\). The area of the base \(A=\frac{1}{2}\times b\times h\).

$$ A=\frac{1}{2}\times6\times5 = 15\space cm^{2} $$

The height of the prism (length of the bottle) \(l = 8\space cm\). So the volume of one - bottle \(V=A\times l\)

$$ V = 15\times8=120\space cm^{3} $$

Step2: Calculate the number of bottles

Let \(n\) be the number of bottles. We know that the total volume of cologne is \(V_{total}=4800\space cm^{3}\). Using the formula \(n=\frac{V_{total}}{V}\) (where \(V\) is the volume of one bottle)

$$ n=\frac{4800}{120}=40 $$

Answer:

\(40\)