Question

a factory makes bottled cologne. each bottle is in the shape of a triangular prism, as shown below. if the factory used 10,800 \\(\mathrm{cm}^3\\) of cologne, how many bottles did the factory fill with cologne? 9 cm 5 cm 8 cm \\(\square\\) bottles

Explanation:

Step1: Find area of triangular base

The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. Here, base = 5 cm, height = 8 cm.
$\text{Area of base} = \frac{1}{2} \times 5 \times 8 = 20 \ \text{cm}^2$

Step2: Calculate volume of 1 bottle

Volume of a prism is $\text{Area of base} \times \text{length of prism}$. The prism length is 9 cm.
$\text{Volume per bottle} = 20 \times 9 = 180 \ \text{cm}^3$

Step3: Find number of bottles

Divide total cologne used by volume per bottle.
$\text{Number of bottles} = \frac{10800}{180}$

Answer:

60 bottles