Sure, let's solve this step-by-step:
1. Understand the given information:
- The mass per cubic centimeter (cm³) of the channel is given as 7.5 grams.
- We need to calculate the mass of a 1 meter (m) length of the channel.
2. Convert the length from meters to centimeters:
- Since 1 meter equals 100 centimeters, we have:
[tex]\[
\text{Length} = 1 \text{ meter} = 100 \text{ centimeters}
\][/tex]
3. Calculate the volume of the channel:
- We assume that the cross-sectional area of the channel remains constant and it sums up to 1 square centimeter as we are not given any specific dimensions of the shape of the channel. Therefore, the volume V of the channel for a length of 100 centimeters is:
[tex]\[
V = \text{Area} \times \text{Length} = 1 \text{ cm}^2 \times 100 \text{ cm} = 100 \text{ cm}^3
\][/tex]
4. Find the mass of the channel:
- Given that each cubic centimeter has a mass of 7.5 grams, we can multiply the total volume by the mass per unit volume to find the total mass:
[tex]\[
\text{Mass} = \text{Volume} \times \text{Mass per unit volume}
\][/tex]
[tex]\[
\text{Mass} = 100 \text{ cm}^3 \times 7.5 \text{ grams per cm}^3 = 750 \text{ grams}
\][/tex]
Therefore, the mass of a 1-meter length of the channel is 750 grams.
