Question

a factory makes bottled perfume. each bottle is in the shape of a triangular prism, as shown below. if the factory is filling 42 such bottles, how much perfume will the factory need (in cubic centimeters)?

Explanation:

Step1: Find volume of one triangular prism

The formula for the volume of a triangular prism is $V = \frac{1}{2} \times base \times height \times length$. Here, base = 7 cm, height = 6 cm, length = 8 cm.
So, $V_{one} = \frac{1}{2} \times 7 \times 6 \times 8$
First, calculate $\frac{1}{2} \times 7 \times 6 = 21$, then $21 \times 8 = 168$ cubic centimeters. So one bottle has a volume of 168 $cm^3$.

Step2: Find total volume for 42 bottles

Multiply the volume of one bottle by 42. So $V_{total} = 168 \times 42$
Calculate $168 \times 42$: 16840=6720, 1682=336, then 6720+336=7056.

Answer:

7056 cubic centimeters