Question

a factory makes bottled cologne. each bottle is in the shape of a triangular prism, as shown below. if the factory used 7056 \\( \mathrm{cm}^3 \\) of cologne, how many bottles did the factory fill with cologne?

image of a triangular prism with base triangle having base 7 cm, height 6 cm, and the prism height 8 cm

text box for answer: \\( \square \\) bottles buttons: refresh, check

Explanation:

Step1: Calculate volume of triangular prism

The formula for the volume \( V \) of a triangular prism is \( V=\frac{1}{2}\times\text{base}\times\text{height of triangle}\times\text{length of prism} \). Here, base of triangle is \( 7\space\text{cm} \), height of triangle is \( 6\space\text{cm} \), and length of prism is \( 8\space\text{cm} \). So, \( V = \frac{1}{2}\times7\times6\times8 \). First, \( \frac{1}{2}\times7\times6 = 21 \), then \( 21\times8 = 168\space\text{cm}^3 \).

Step2: Find number of bottles

Total volume of cologne is \( 7056\space\text{cm}^3 \). Number of bottles \( n=\frac{\text{Total Volume}}{\text{Volume per bottle}}=\frac{7056}{168} \). Dividing, \( 7056\div168 = 42 \).

Answer:

42